NSF Focused Research Group:

Wavelets, Frames, and Operator Theory

This FRG will enhance collaboration among the members by:

  • holding regular think-tank-style workshops,

  • involving students and postdocs in those workshops,

  • exchanging students for short visits among the Principal Investigators,

  • forming project subgroups to attack specific problem areas.


Contents

   A sample of the FRG research problems

   Project areas

   Participants

   Events (upcoming events in red)

   Reports


A sample of the FRG research problems:

  • Definition: A subset MATH is said to be a wavelet set for an expansive integral $d\times d$ matrix $A$ if the inverse Fourier transform $\psi $ of MATH is a wavelet, i.e., if the double indexed family MATH, $j\in \QTR{Bbb}{Z}$, MATH, is an orthonormal basis for MATH. (This is equivalent to $\Omega $ tiling $\QTR{Bbb}{R}^{d}$ both under the translations MATH and the scalings MATH.)

  • Problem A: Wavelet set implementation. Because of the structure of wavelet sets, their explicit constructions, and the potential usefulness of dealing with only one wavelet in higher dimensions, there are two immediate and natural problems. We wish to develop recursive programmable schemes for applications, cf. [BT93, Stro00a, Wic94], as well as a theoretical formulation in terms of frames, cf. [HL00, Han97].

    This latter approach would sacrifice orthonormality, which is often not a sacrifice in applications dealing with noise reduction and stable representation. On the other hand, the frame theoretic approach would reduce the recursive complexity, it would add smoothness in the spectral domain, and it would provide an iterative method of signal reconstruction. Related to this whole issue is the necessity of a critical comparison of the geometrical constructions in [BS01] and the theoretical but constructive approach in [BMM99] in terms of multiplicity functions and finite von Neumann algebras.

    Further, the examples of wavelet sets are typically fractal-like, in the sense that the sets are given as limits of infinite processes. Numerically, this could pose difficulties. Consequently, one may seek wavelet sets that are, for example, finite unions of rectangles. In this regard, Merrill has discovered a family of multiwavelets (with multiplicity 2 in 2 dimensions) of this type, cf. the geometric examples after the complete iteration in [DL98].

    [BMM99] L.W. Baggett, H. A. Medina, and K. D. Merrill, Generalized multi-resolution analysis, and a construction procedure for all wavelet sets in Rn, J. Fourier Anal. Appl., 5 (1999), 563-573.

    [BS01] J. J. Benedetto and S. Sumetkijakan, A fractal set constructed from a class of wavelet sets, Inverse problems, image analysis, and medical imaging (New Orleans, LA, 2001) (M. Zuhair Nashed and Otmar Scherzer, eds.), Contemporary Mathematics, vol. 313, American Mathematical Society, Providence, RI, 2002, pp. 19-35.

    [BT93] J. J. Benedetto and A. Teolis, A wavelet auditory model and data compression, Appl. Comput. Harmon. Analy., 1 (1993), 3-28.

    [DL98] X. Dai and D. R. Larson, Wandering vectors for unitary systems and orthogonal wavelets, Mem. Amer. Math. Soc., 134 (1998), no. 640.

    [Han97] B. Han, On dual wavelet tight frames, Appl. Comput. Harmon. Anal., 4 (1997), 380-413.

    [HL00] D. Han and D. R. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc., 147 (2000), no. 697.

    [Stro00a] T. Strohmer, Numerical analysis of the non-uniform sampling problem, J. Comput. Appl. Math., 122 (2000), 297-316.

    [Wic94] M. V. Wickerhauser, Adapted Wavelet Analysis from Theory to Software, A K Peters Ltd., Wellesley, MA, 1994.

  • Definition: (see [JoPe92]) A measurable set $\Omega $ in $\QTR{Bbb}{R}^{d}$, of finite positive measure, is said to be a spectral set if MATH has an orthogonal basis of real exponentials MATH for a subset $\Lambda $ of points MATH. If an orthogonal basis MATH exists, $\Lambda $ is called a spectrum. $\Omega $ is said to be a tiling if it can be made to tile $\QTR{Bbb}{R}^{d}$ using only translations.

    [JoPe92] P. E. T. Jorgensen and S. Pedersen, Spectral theory for Borel sets in $\QTR{Bbb}{R}^{n}$ of finite measure, J. Funct. Anal., 107 (1992), 72-104.

  • Problem B: Spectra-Tilings Conjecture. Let MATH with MATH. If $\Omega $ is a spectral set, then $\Omega $ tiles $\QTR{Bbb}{R}^{d}$ by translation. Further, there is a one-to-one correspondence between the spectra of $\Omega $ and the set of tilings of $\Omega $.

    The Fuglede conjecture, in its original primitive form, is 40 years old, but it has come to signify a much more general principle: It is now used to describe any one of several correspondences between spectrum and geometry, much in the spirit of Mark Kac's "Can you hear the shape of a drum?" theme. In its original form, the Fuglede conjecture states that an open set S of finite positive measure in Rd admits a Fourier basis F if and only if it tiles Rd with translations. This form of the conjecture is still open, but it is recognized as being difficult, involving combinatorics and number theory. A number of serious attempts at counterexamples have not succeeded. But in many applications, more detailed information is available about the context of the problem: If for example S is known to be the finite union of non-overlapping intervals, then the possible spectral pairs (S,F) are of significance in combinatorics and in sampling problems. Therefore much effort in the FRG has been focused on cases when S is already known to satisfy both the basis condition and the tile condition. Then the question is the correspondence between spectrum and tile-translations, or more generally between spectrum and geometry. This is "the generalized Fuglede conjecture", and it has been extraordinarily fruitful. The simplest case arises when the vectors that produce a Fourier basis are also translation vectors in a tiling. Several of us in the FRG have published papers on this: For example, if S is the d-cube, members in the FRG and their co-workers showed that the frequencies F in a Fourier basis and the vectors V that make S tile coincide, i.e., F = V, and when d = 3, we found the possibilities for F. Equivalently, (S,F) is a spectral pair if and only if (S,F) is a tile system. But spectral/tile duality is a central theme in many wavelet problems, in iterated function systems, in spectral theory for Hilbert spaces built from Hausdorff measure Hs, of fractional dimension s. They are central in harmonic analysis, see for example the websites of Terence Tao and I. Laba, and this FRG website. In its general form, the Fuglede conjecture is central to how we construct wavelet bases, and Gabor frames. In the FRG, Jorgensen and his Ph.D. student D. Dutkay proved that the spectral/tile principle applies to Hs, Hausdorff measure, 0 < s < 1, and that the duality principle lets us write down wavelet bases in Hs-Hilbert spaces. Even for the middle-third Cantor set, this is new and significant. The middle-third Cantor set is one of the fractals which does not have a Fourier basis. Many others do! (A sample of researchers connected to the FRG and with papers on the subject: Palle Jorgensen, Steen Pedersen, Yang Wang, Jeff Lagarias, Izabella Laba, Alex Iosevich, Terence Tao,... A sample of papers as of May 15, 2003: [B1]-[B14] below.) Research on exact harmonic analysis-duality principles in geometric measure theory are still in their infancy. But there is a lot of interest in this. Note that R. Strichartz's NSF-funded undergraduate research projects have this focus. We plan to continue to work with Strichartz and his team in this direction.

    This circle of problems around the Fuglede conjecture is not isolated. Don't think of math as finite. Rather: "Infinite in all directions", is more like it! We usually see that each answered question opens up three new questions. That is especially true for the good problems in math. (Hmm...!, it would sound like math is not efficient, but the good stuff is what we learn from solutions to problems! Perhaps more so than the problems themselves.) Anyway what we call "The Fuglede problem", or conjecture (I forgot when it was elevated to a conjecture!) is in fact many problems..! A major theme in math is that of understanding connections between geometry (for example tiling) and some kind of spectrum. What I learned from the last wonderful Terence Tao paper, and papers of others, is that it may be possible to do some kind of functor from geometry to an "easier" setup (finite combinatorics and algebra) involving only certain finite cyclic groups G. When is this is successful? If the assignment is a functor! We have to be able to get an implication like this: Within the spectral setting coming from a suitable Hadamard matrix, verify the implication: "No solution in the finite case (a particular Gd for some d)" implies "no solution to the original problem!" The original problem here is the tiling question. Looked at this way, we are just scratching the tip of an ice-berg.

    [B1] D. Dutkay, P. Jorgensen, Wavelets on fractals, preprint June 2003, Univ. of Iowa, submitted to Revista Matemática Iberoamericana.

    [B2] B. Fuglede, Commuting self-adjoint partial differential operators and a group-theoretic problem, J. Funct. Anal. 16 (1974), 101-121.

    [B3] A. Granville, I. Laba, Y. Wang, On finite sets which tile the integers, Preprint Dec 19, 2001.

    [B4] A. Iosevich, N. Katz, T. Tao, Convex bodies with a point of curvature do not have Fourier bases, Amer. J. Math. 123 (2001), 115-120.

    [B5] A. Iosevich, S. Pedersen, Spectral and tiling properties of the unit cube, Internat. Math. Res. Notices 1998 (1998), no. 16, 819-828.

    [B6] P. Jorgensen, Spectral theory of finite-volume domains in Rn, Adv. in Math. 44 (1982), 105-120.

    [B7] P. Jorgensen, S. Pedersen, Spectral theory for Borel sets in Rn of finite measure, J. Funct Anal. 107 (1992), 72-104.

    [B8] P. Jorgensen, S. Pedersen, Spectral pairs in Cartesian coordinates, J. Fourier Anal. Appl. 5 (1999), 285-302.

    [B9] I. Laba, Fuglede's conjecture for a union of two intervals, Proc. Amer. Math. Soc. 129 (2001), 2965--2972.

    [B10] J.C. Lagarias, J.A. Reeds, Y. Wang, Orthonormal bases of exponentials for the n-cube, Duke Math. J. 103 (2000), 25-37.

    [B11] J.C. Lagarias, Y. Wang, Tiling the line with translates of one tile, Invent. Math. 124 (1996), 341-365.

    [B12] S. Pedersen, Y. Wang, Universal spectra, universal tiling sets and the spectral set conjecture, Math. Scand. 88 (2001), 246--256.

    [B13] Y. Wang, Wavelets, tiling, and spectral sets, Duke Math. J. 114 (2002), 43--57.

    [B14] Y. Liu and Y. Wang, The uniformity of non-uniform Gabor bases, Adv. Comput. Math. 18 (2003), no. 2--4 (special issue on Frames edited by A. Aldroubi and Q. Sun), 345--355.

  • Problem C: Irregular Translations. The result of Wang [Wan01] on admissible translation and dilation sets for wavelets arising from wavelet sets shows that these sets can be irregular. The same has not been studied for other type of wavelets. What if we change the wavelet set condition to Meyer wavelets? What about compactly supported wavelets and MRA wavelets? Wang's approach differs substantially from the approaches in [LWWW02] and [Füh01]. Could it be used to study the admissible dilation sets in a continuous wavelet transform? How could an multiresolution analysis be defined with more than one scaling factor? If so, will there be potential for new applications? The members of the FRG have much combined expertise in areas related to wavelets, wavelet sets, and irregular sampling. In particular, Larson was the first to study wavelet sets, Aldroubi, Benedetto and Heil have extensive expertise in irregular sampling and MRA wavelets, and Jorgensen and Ólafsson have studied wavelets and wavelet sets from the point of view of representation theory, which may offer another important insight into this problem.

    [Füh01] H. Führ, Admissible vectors for the regular representation, Proc. Amer. Math. Soc. 130 (2002), no. 10, 2959-2970 (electronic).

    [LWWW02] R. S. Laugesen, N. Weaver, G. Weiss and E. Wilson, A characterization of the higher dimensional groups associated with continuous wavelets, J. Geom. Anal. 12 (2002), no. 1, 89-102.

    [Wan01] Y. Wang, Wavelets, tiling and spectral sets, Duke Math. J. 114 (2002), no. 1, 43-57.

Project areas:

Participants:

FRG member: Specialties: Grad students:
Akram Aldroubi
Vanderbilt University
Wavelets, frames, sampling theory, signal/image processing, biomedicine Armando Rodado
Lawrence W. Baggett
University of Colorado
Harmonic analysis, representation theory, wavelets and generalized multiresolution analyses Toby Fernsler
John J. Benedetto
University of Maryland
Classical harmonic analysis, frames and wavelet theory, sampling theory, speech compression, periodicity detection Joseph Kolesar, Alex Powell, and Juan Romero
Christopher E. Heil
Georgia Institute of Technology
Time-frequency analysis, frames, pseudodifferential operators, MRA multiwavelets Kasso Okoudjou
Palle E.T. Jorgensen
University of Iowa
Operator theory, spectral theory, spectrum-tile duality, qubit algorithms, mathematical physics, symbolic dynamics Dorin Dutkay and Paul Johnson
David R. Larson
Texas A&M University
Operator algebras, operator theory, wavelets, frames, functional analysis, applied harmonic analysis Troy Henderson and Scott Armstrong
Gestur Ólafsson
Louisiana State University
Harmonic analysis and representation theory, special functions, orthogonal polynomials Troels Johansen and Imitiaz Hossain
Yang Wang
Georgia Institute of Technology
Self-similarity, tiling, fractal geometry, spectral sets, wavelets  

Events (upcoming events in red):

FRG-meetings, workshops, consultations, and collaborations:
July 1-7, 2002 University of Colorado, Boulder
Workshop: L. Baggett, P. Jorgensen, K. Merrill, J. Packer: "Tiling theory, spectral sets, and the Fuglede Conjecture." Research for the paper "Transitive actions of groups of unitary matrix functions on resolution subspaces of L2(Rd) with multiple generators"
 
July 12-21, 2002 Workshop: "Tiling theory, spectral sets, and the Fuglede conjecture". Organizer, David R. Larson
Location: Texas A&M University
Ten-day workshop
Problems discussed
October 2002 Vanderbilt University
Five-day workshop
Postponed. Details and dates to be announced.
 
January 19-21, 2003 Workshop II: "Modulation spaces and the continuous wavelet transform". Organizer, J. Benedetto.
Location: University of Maryland, College Park.
--The dates for the UMD workshop, immediately following the 2003 Annual Meeting of the AMS (Baltimore, January 1518, 2003):
   Sunday, January 19, 2003, afternoon session;
   Monday, January 20, 2003 (MLK Holiday), morning and afternoon sessions;
   Tuesday, January 21, 2003, morning session.
For information on the Special Session on Wavelets, Frames and Operator Theory organized by C. Heil, P. Jorgensen, and D. Larson at the 2003 Annual Meeting of the AMS, click here.
 
March 12-16, 2003 Workshop III: "Modulation spaces, wavelet sets, and the Fuglede conjecture". Organizer, G. Ólafsson.
Location: Louisiana State University, Baton Rouge.
Five-day workshop on Wavelets and Frames, prior to the AMS sectional meeting (Baton Rouge, March 14-16, 2003)
--The dates for the LSU workshop, before and during the 2003 Spring Southeastern Sectional Meeting of the AMS (Baton Rouge, LA, March 1416, 2003):
   Wednesday, March 12, 2003, morning and afternoon sessions;
   Thursday, March 13, 2003, morning sesstion, noon FRG meeting, and afternoon discussion;
   Friday, March 14-Sunday, March 16, 2003, the workshop becomes a part of the Special Session on Frames, Wavelets, and Tomography at the AMS meeting in Baton Rouge.
For information on the Special Session on Frames, Wavelets, and Tomography organized by G. Ólafsson at the AMS Sectional Meeting, Baton Rouge, March 14-16, 2003, click here.
 
May 11-13, 2003 Workshop: "The Fuglede conjecture and Gabor frame theory". Organizer, Akram Aldroubi
Location: Vanderbilt University, Nashville, TN
Three-day workshop
   Tutorial 1: "Excess and density of frames", Chris Heil.
   Tutorial 2: "Fuglede conjecture or related topics", Yang Wang.
   Tutorial 3: "Fuglede conjecture", Palle Jorgensen and Steen Pedersen.
   Problem sessions: Participant can present problems they wish to discuss.
   Collaborative research; Group can form and small seminar rooms will be available for groups who wish to discuss possible new collaborations or continue ongoing collaborations.
Following the workshop, there is International Conference on Advances in Constructive Approximation, Nashville, May 14-17, 2003 (John Benedetto will be giving one of the main talk at this conference).
 
June 23 - July 2, 2003 Workshop: "Three wavelet themes". Organizer, Lawrence Baggett.
Location: University of Colorado, Boulder
Ten-day workshop
   Theme 1: "Wavelet sets, and techniques for their construction", L. Baggett, J. Benedetto, and K. Merrill.
   Theme 2: "Modulation spaces", C. Heil.
   Theme 3: "Wavelet frames on irregular grids and nonharmonic Gabor systems", A. Aldroubi.
These tutorials, listed below as three-hour blocks, will of course include breaks when needed. There will also be ample time for subsets of participants to work together on private projects, and some people may wish to give more formal talks. These will be arranged during the workshop.
   Monday June 23: 9am - noon, Theme 1. 2pm - 5pm, Theme 2. 6pm: Party at Larry and Christy's. (Directions later.)
   Tuesday June 24: 9am - noon, Theme 1. 2pm - 4pm, Theme 2. 4pm-5pm: Brief summaries of selected FRG projects. 5pm - 6pm, meeting of the FRG members with Joe Jenkins.
   Wednesday June 25: 9am - noon, Theme 1. 2pm - 5pm, Theme 2.
   Thursday June 26: 9am - noon, Theme 3. 2pm - 5pm, Theme 3.
   Friday June 27: 9am - noon, Theme 3. 2pm - 5pm, Contributed talks (TBA).
   Saturday and Sunday June 28 and 29, free time. Private projects, extra talks, hiking, touring,...
   Monday June 30: Revisit theme 1, discussions, problem sessions, other talks.
   Tuesday July 1: Revisit theme 2, discussions, problem sessions, other talks.
   Wednesday July 2: Revisit theme 3, discussions, problem sessions, other talks.
Participants: Alex Powell, Ed Wilson, Guido Weiss, Keri Kornelson, Gestur Ólafsson, Pete Casazza, Palle Jorgensen, Eric Weber, John Benedetto, Judy Packer, Radu Balan, Brad Ulrich, Casey Leonetti, Juan Romero, Marcin Bownik, Ozgur Yilmaz, Wayne Lawton, Wojtek Czaja, Akram Aldroubi, Dorin Dutkay, Matt Fickus, Chris Heil, Kathy Merrill, David Larson, Yang Wang, Vera Furst, Kasso Okoudjou, Norbert Kaiblinger, Francois Meyer, Steen Pedersen, Jim Daly, Keith Phillips, Josip Derado, Brody Johnson.
 
October 11-14, 2003 Workshop: " ". Organizers, Christopher E. Heil, Yang Wang.
Location: Georgia Tech
Tentative schedule:
   Saturday, Oct. 11: 2:00-4:00 Tutorial by Yuesheng Xu.
   Sunday, Oct. 12: 9:30-12:00 Tutorial by Guowei Wei; 3:00-5:00 Tutorial by Guowei Wei.
   Monday, Oct. 13: 9:30-12:00 Tutorial by Gestur Ólafsson; 3:00-5:00 Tutorial by Gestur Ólafsson.
   Tue, Oct 14: 9:30-12:00 Tutorial by Yuesheng Xu.
Participants: Lawrence Baggett, Eugene Belogay, Bernhard Bodmann, Dorin Dutkay, Vera Furst, Bin Han, Deguang Han, Palle Jorgensen, Keri Kornelson, Mark Lammers, Gestur Ólafsson, Manos Papadakis, Darrin Speegle, Qiyu Sun, Guowei Wei, Victor Wickerhauser, Yuesheng Xu, Ozgur Yilmaz, and local Georgia Tech people: Xinrong Dai, DJ Feng, Jeff Geronimo, Christopher Heil, Christian Houdré, Norbert Kaiblinger, Sandie Leach, Becky Upchurch, Yang Wang, Long Wang, Hao Min Zhou.
 
February 15-21, 2004 Miniworkshop: "Wavelets and Frames".
Location: Mathematisches Forschungsinstitut Oberwolfach, Lorenzenhof, Oberwolfach-Walke, Germany.
Organizers: Hans G. Feichtinger, Professor, Institute of Mathematics, University of Vienna, hans.feichtinger@univie.ac.at; Palle E.T. Jorgensen, Professor, Department of Mathematics, The University of Iowa, jorgen@math.uiowa.edu; Dave Larson, Professor, Department of Mathematics, Texas A&M, larson@math.tamu.edu; Gestur Ólafsson, Professor, Department of Mathematics, Louisiana State University, olafsson@math.lsu.edu.
Workshop introduction Duality principles in analysis
Spring 2004 Workshop. Organizer, Palle E.T . Jorgensen
Location: University of Iowa, Iowa City, IA
In a slight abuse of geography, this workshop was subsumed in the Oberwolfach miniworkshop above.
 
July 2004 Workshop: " ". Organizer, J. Benedetto.
Location: University of Maryland, College Park.
Ten-day workshop
 
Fall 2004 Workshop: " ". Organizer, G. Ólafsson.
Location: Louisiana State University, Baton Rouge.
Workshop
 
Spring 2005 Workshop: " ". Organizer, Akram Aldroubi
Location: Vanderbilt University, Nashville, TN
Workshop
 

Meetings and conferences where one or more members of this NSF Focused Research Group is an organizer or a speaker:
5th Joint IDR-IMA Workshop
April 9-13, 2001
Organizers: Ronald DeVore, Amos Ron, Patrick Van Fleet.
Location: Institute for Mathematics and its Applications (IMA), University of Minnesota, Minneapolis
Abstracts: Aldroubi, Heil, Jorgensen, Larson.
Pictures of Jorgensen and Larson speaking and in the audience.
AMS Meeting #982
November 9-10, 2002
AMS Special Session: Functional and Harmonic Analysis of Wavelets, Frames and Their Applications.
Organizers: D. Han and M. Papadakis.
Location: University of Central Florida
AMS Meeting #983: the
 annual AMS winter meeting
January 15-18, 2003
AMS Special Session: Wavelets, Frames and Operator Theory.
Organizers: C. Heil, P. Jorgensen, and D. Larson.
Location: Baltimore, Maryland
AMS Meeting #984
March 14-16, 2003
AMS Special Session: Frames, Wavelets and Tomography.
Organizer: G. Ólafsson.
Location: Louisiana State University, Baton Rouge, LA
June 15-22, 2003 European Conference: Functional Analysis VIII
Location: Dubrovnik, Croatia

"Functional Analysis VIII" is a conference and a postgraduate school on functional analysis, and related fields, with several more or less independent parts dealing with various aspects of functional analysis (operator algebras, probability theory, harmonic analysis, wavelets, representation theory...). The program will include series of lectures, single lectures and short communications.

The conference will be held in Dubrovnik, June 15-22, 2003 at the "Inter-University Centre". This will be the eighth meeting; the first seven were held in 1981, 1985, 1989, 1993, 1997, 1999 and 2001. Most of the main lectures were published in Springer Verlag Lecture Notes (issues 948 and 1242) and in Various Publication Series of the Aarhus University (issues 40, 43, 44 and 45).

The organizers are: Hrvoje Kraljevic, Davor Butkovic, Murali Rao, Damir Bakic, Pavle Pandzic, Hrvoje Sikic and Zoran Vondracek.

Some of the invited plenary speakers: Palle T. Jorgensen, Univ. of Iowa, USA; Bojan Magajna, Univ. of Ljubljana, Slovenia; Vladimir M. Manuilov, Moscow State Univ., Russia; Klaus Thomsen, Univ. of Aarhus, Danmark; J.D. Maitland Wright, Univ. of Reading, UK; Dubravka Ban, University of Split, Croatia and Southern Illinois University, Carbondale, USA; Peter Bantay, Eötvös Lorand Univ., Budapest, Hungary; Dan Barbasch, Cornell University, USA; Corinne Blondel, University Paris 7, France; Mladen Bozicevic, University of Zagreb, Croatia; William Casselman, University of British Columbia, Canada; Henry Kim, Univ. of Toronto, Canada; Atsushi Matsuo, Dept. of Math. Sciences, Univ. of Tokyo, Japan; Dragan Milicic, University of Utah, USA; Allen Moy, HKUST, Hong Kong, China; David Vogan, M.I.T., USA; David R. Larson, Texas A&M University, USA; Darrin Speegle, Univ. of St. Louis, USA

Part of the Program:

Monday, June 16, 2003 8:45-9:00 Opening ceremony 9:00-9:45 D.R.Larson Operators, wavelets and frames I ..............

Tuesday, June 17, 2003
9:00-9:45 P.E.T. Jorgensen Some connections between operator theory and wavelet analysis I
9:55-10:40 D.R. Larson Operators, wavelets and frames II
11:00-11:45 D. Speegle Wavelet constructions in Rn I ............

Wednesday, June 18, 2003
9:00-9:45 W. Schachermayer Optimal investment strategies in incomplete financial markets III ................

Thursday, June 19, 2003
15:10-15:55 P.E.T. Jorgensen Some connections between operator theory and wavelet analysis II

Friday, June 20, 2003
9:55-10:40 P.E.T. Jorgensen Some connections between operator theory and wavelet analysis III
11:00-11:45 D. Barbasch The role of unipotent representations in the classification of the unitary dual of a reductive group III .............

Saturday, June 21, 2003
9:55-10:40 P.E.T. Jorgensen Some connections between operator theory and wavelet analysis IV
11:00-11:45 D.R.Larson Operators, wavelets and frames IV ................

May 24-30, 2004 Second International Conference on Computational Harmonic Analysis in conjunction with the 19th Annual Shanks Lecture Honoring Baylis and Olivia Shanks: conference web page (or see the Wavelet Digest announcement).
Organizers: Akram Aldroubi, Charles Chui, Emmanuelle Candes, Richard Baraniuk, Francois Meyer, Thomas Strohmer, Hamid Krim, Bruno Torresani, Douglas Hardin, Ed Saff.
Location: Vanderbilt University, Nashville Tennessee.
Abstract of Jorgensen's talk

Reports:

First annual report (June 2003)



Work displayed on this page was supported in part by the U.S. National Science Foundation under grants DMS-9987777 and DMS-0139473(FRG).

This page was last modified on 2 Apr 2004 by Brian Treadway.


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