[Half of a Family of Five + Greta] [Wavelet Decomposed Jorgensen] Palle Jorgensen     

Professor    CV (2 pg.)    CV (5 pg.)

Department of Mathematics

The University of Iowa

Also affiliated with

the interdisciplinary Ph.D. program in
Applied Mathematical and Computational Sciences
Office Email Paper Mail Phone
25B jorgen@math.uiowa.edu Palle Jorgensen
Department of Mathematics   
14 MLH
The University of Iowa
Iowa City, IA 52242-1419
USA 		voice: 319-335-0782
fax: 319-335-0627

Current Courses

22M:313 (Fall 2006)

22M:210 (Fall 2007)

22M:313 (Fall 2007)

New Books

Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics

Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics

by Palle E. T. Jorgensen

Link to Other Books by Palle E. T. Jorgensen on Amazon

Textbook (2006): Springer GTM 234

Analysis and Probability: Wavelets, Signals, Fractals

Wavelet Book (2002)

Wavelets through a Looking Glass: The World of the Spectrum

Textbook in Springer's Graduate Texts in Mathematics series

[cover of Analysis and Probability: Wavelets, Signals, Fractals]

Analysis and Probability:
Wavelets, Signals, Fractals

by Palle E. T. Jorgensen

Graduate Texts in Mathematics, Vol. 234, Springer

As of 9/18/2006, this new book is in the warehouse and is being shipped to bookstores.


Link to the Wavelet Decomposition Images

Wavelet book in Birkhäuser's Applied and Numerical Harmonic Analysis series

[cover of Wavelets through a Looking Glass: The World of the Spectrum]

Wavelets through a Looking Glass: The World of the Spectrum

by Ola Bratteli and Palle E. T. Jorgensen

Applied and Numerical Harmonic Analysis, Birkhäuser, 2002

Announcement of a New Research Journal

Complex Analysis and Operator Theory

Other Research Journals

of which Palle E.T. Jorgensen is an editor

Recent and Upcoming Conferences

An engineering friend described the old approach to data mining as "Just drop a computer down onto a gigantic set of unstructured numbers!" About the Book
Analysis and Probability:
Wavelets, Signals, Fractals

by Palle E. T. Jorgensen

Graduate Texts in Mathematics, Vol. 234, Springer

As of 9/18/2006, this new book is in the warehouse and is being shipped to bookstores.

Excerpts [PDF files]:

   Opening pages, including dedication, preface, table of contents, frontispiece ("Just drop a computer down...!"), and an apology

   Full Bibliography and Index

Pre-release announcements:
CAM-Digest
The Wavelet Digest
Books on wavelets

The book Analysis and Probability: Wavelets, Signals, Fractals, by Palle E. T. Jorgensen, is on sale at:

 Prairie Lights (Iowa City)  Iowa Book & Supply  University of Iowa Bookstore
 Seminary Co-op  Powell's  Yurinsha Book News
 AllBookStores.com  Blackwell's  << (search ISBN 0387295194)
 Springer (N.Y.)    
 Amazon.com (U.S.)    Amazon.co.jp (Japan)

with apologies to Edvard Munch About the Book
Wavelets through a Looking Glass:
The World of the Spectrum

by Ola Bratteli and Palle E. T. Jorgensen

Applied and Numerical Harmonic Analysis, Birkhäuser, 2002

Comments by Yves Meyer

Reviews on Amazon.com by Ivan Avramidi, L.M. Schmitt, Akram Aldroubi, William Arveson, and Mark A. Pinsky (subsets of these reviews are also found at the clone sites ReviewIndex.com, BooksUnderReview.com, MathBook.com, Rbookshop.com, BookFinder4U.com, and AnyBook4Less.com.)

Review in Mathematical Reviews by Gilbert Walter

Review in Zentralblatt Math. by Ole Christensen

Review in SIAM Review by Judith A. Packer

Listings on Springer NY and Birkhäuser Boston web sites

Birkhäuser advance flyer [PDF file]

Corrections

Excerpts [PDF files]:

   Opening pages, including cover, dedication, frontispiece, and Table of Contents

   First chapter, including Section 1.3 on the quantum computer algorithm for wavelets
      ("Qubits: The oracle of Feynman and the algorithm of Shor")
         and Section 1.4 ("Chaos and cascade approximation"), where the
            illustration above of "The Scream" among wavelets and spinors appears

   Full Bibliography and Index

 

Wavelets with fixed support are known to vary with parameters, and they can be viewed in motion in
A flip-book of wavelets on the interval [0,5] and their associated scaling functions [large PDF file]. 		Compare Wim Sweldens's Wavelet Cascade Applet Two-parameter family of compactly supported wavelets

About the Book Cover, the Dedication, and Yosemite

 		[cover of Wavelets through a Looking Glass: The World of the Spectrum]

The book Wavelets through a Looking Glass: The World of the Spectrum, by O. Bratteli and P. Jorgensen, is on sale at:

 Prairie Lights (Iowa City)  Yurinsha Book News  
 Buy.com  Seminary Co-op  Walmart
 Barnes & Noble (used)  Abebooks.com  Alibris
 Barnes & Noble  Chapters (Canada)  Bokfynd.nu (Sweden)
 Springer (N.Y.)  Birkhäuser (Boston)  
 Amazon.com (U.S.)  Amazon.co.uk (U.K.)  Amazon.fr (France)
 Amazon.de (Germany/Austria)  Amazon.ca (Canada)  Amazon.co.jp (Japan)
 A1Books  Blackwell's  << (search ISBN 0817642803)
See also Allbookstores.com (where it is a BESTSELLER in two categories, one of which is apt)
or Bookchecker.com or Bookfinder.com or Bublos.com or AddALL.com or Half.com or aaabooksearch.com or booksprice.com to compare prices at various online bookstores
(but check with the stores directly: some data are out of date).
If you have any problems with your order, send me an e-mail at jorgen@math.uiowa.edu.

About Me

Quotes

Featured Reviews

My Other Books

Some of Jorgensen's Publications in 2010

P. E. T. Jorgensen and M.-S. Song, "Matrix Factorization and Lifting,", submitted, 2010. pdf

Affine Fractals as Boundaries and Their Harmonic Analysis
D. E. Dutkay, P.E.T. Jorgensen, submitted

Functional Analysis
F. Tian, P.E.T. Jorgensen, submitted

Spectral measures and Cuntz algebras
D. E. Dutkay, P.E.T. Jorgensen, submitted

Some of Jorgensen's Publications in 2009

P. E. T. Jorgensen and M.-S. Song, "Scaling, image compression and encoding,", submitted, 2009. pdf

P. E. T. Jorgensen and M.-S. Song, "Spectral Theory of Discrete Processes," Cent. Eur. J. Phys. 8(3):340-363, 2010. pdf

P. E. T. Jorgensen and M.-S. Song, "An Extension of Wiener Integration with the Use of Operator Theory," J. Math. Phys. 50 103502, 2009. pdf

P. E. T. Jorgensen and M.-S. Song, "Analysis of Fractals, Image Compression, Entropy Encoding and Karhunen-Loeve Transforms," Acta Appli candae Mathematica, 108, 5:498-508, Springer, 2009. pdf

Families of spectral sets for Bernoulli convolutions
P.E.T. Jorgensen, K. Kornelson, K. Shuman, submitted

Fourier Duality for Fractals Measures with Affine Scales
D. E. Dutkay, P.E.T. Jorgensen, submitted.

Spectral Reciprocity and Matrix Representations of Unbounded Operators
P.E.T. Jorgensen, E. P. J. Pearse, submitted.

On Common Fundamental Domains
D. E. Dutkay, P.E.T. Jorgensen, D. Han, G. Picioroaga, submitted.

Spectral Operator Theory of Electrical Resistance Networds
P.E.T. Jorgensen, E. P. J. Pearse, submitted.

Some of Jorgensen's Publications in 2008

Spectral Theory for Discrete Lapacians
by Dorin E. Dutkay and Palle E. T. Jorgensen, , submitted.

Essential selfadjointness of the graph-Laplacian
by Palle E. T. Jorgensen, , submitted.

P. E. T. Jorgensen and M.-S. Song, "Optimal Decompositions of Translations of L^2 - Functions," Complex Analysis and Operator Theory, vo l 3, No 2:449-478, Birkhauser, 2008. pdf

P. E. T. Jorgensen and M.-S. Song, "Comparison of Discrete and Continuous Wavelet Transforms," Springer Encyclopedia of Complexity and S ystems Science, Springer, 2008. pdf

Jorgensen's Publications in 2007

C^*-Algebras Generated by Partial Isometries
by Ilwoo Cho and Palle E. T. Jorgensen, Journal of Mathematical Physics , to appear.


by Palle E. T. Jorgensen and Myung-Sin Song, Complex Analysis and Operator Theory Online First (2007).

Quasiperiodic Spectra and Orthogonality for Iterated Function System Measures
by Dorin E. Dutkay and Palle E. T. Jorgensen, Mathematische Zeitschrift , to appear.

Fourier series on fractals: a parallel with wavelet theory
by Dorin E. Dutkay and Palle E. T. Jorgensen, Mathematische Zeitschrift , to appear.

Affine systems: asymptotics at infinity for fractal measures
by Palle E. T. Jorgensen, Keri A. Kornelson and Karen L. Shuman, Acta Appl. Math. 3 (2007), 181--222.

Unitary Representations of Wavelet Groups and Encoding of Iterated Function Systems in Solenoids
by Dorin E. Dutkay, Palle E. T. Jorgensen and Gabriel Picioroaga, , submitted.

Multiresolution wavelet analysis of integer scale Bessel functions
by Sergio Albeverio, Palle E. T. Jorgensen and Anna M. Paolucci J. Math. Phys. 48 (2007), 073516.

A duality approach to representations of Baumslag-Solitar groups
by Dorin E. Dutkay and Palle E. T. Jorgensen, Contemp. Math , to appear.

Orthogonal Exponentials for Bernoulli Iterated Function Systems
by Palle E. T. Jorgensen, Keri Kornelson and Karen Shuman Representations, Wavelets and Frames A Celebration of the Mathematical Work of Lawrence Baggett (Editors Palle E.T. Jorgensen, Kathy D. Merrill and Judith A. Packer) (2007), 217--238.

The Measure of a Measurement
by Palle E. T. Jorgensen, J. Math. Phys. 48 no. 10 (2007), 103506.

Harmonic analysis of iterated function systems with overlap
by Palle E. T. Jorgensen, Keri A. Kornelson and Karen L. Shuman J. Math. Phys. 48 no. 8 (2007), 083511.

Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
by Palle E. T. Jorgensen and Myung-Sin Song, J. Math. Phys. 48 no. 10 (2007), 103503.

Kadison-Singer from mathematical physics: An introduction
by Palle E. T. Jorgensen, AIM Institute (2007).

Some recent trends from research mathematics and their connections to teaching: Case studies inspired by parallel developments in science and technology
by Palle E. T. Jorgensen,Recent Advances in Computational Sciences: Selected Papers from the International Workshop on Computational Sciences and Its Education, World Scientific Publishing Company (2007).

Jorgensen's Publications in 2006

Kadison-Singer from mathematical physics: An introduction
by Palle E. T. Jorgensen.

Analysis and Probability: Wavelets, Signals, Fractals
by Palle E. T. Jorgensen, Graduate Texts in Mathematics, vol. 234, Springer, New York, 2006, approx. 320 p., 58 illus., hardcover, ISBN 0-387-29519-4.

Wavelets on fractals
by Dorin E. Dutkay and Palle E. T. Jorgensen, Rev. Mat. Iberoamericana 22 (2006), 131--180.

Oversampling generates super-wavelets
by Dorin E. Dutkay and Palle E. T. Jorgensen, Proc. Amer. Math. Soc., to appear.

A non-MRA Cr-frame wavelet with rapid decay
by L.W. Baggett, Palle E.T. Jorgensen, K.D. Merrill, and J.A. Packer, Acta Appl. Math. 89 (2006), 251--270.

Hilbert spaces built on a similarity and on dynamical renormalization
by Dorin E. Dutkay and Palle E. T. Jorgensen, J. Math. Phys. 47 (2006), no. 5, 20 pp.

Harmonic analysis and dynamics for affine iterated function systems
by Dorin E. Dutkay and Palle E. T. Jorgensen, Houston J. Math., to appear.

Methods from multiscale theory and wavelets applied to non-linear dynamics
by Dorin E. Dutkay and Palle E. T. Jorgensen, Wavelets, Multiscale Systems and Hypercomplex Analysis (D. Alpay, ed.), Oper. Theory Adv. Appl., vol. 167, Birkhäuser, Boston, 2006, pp. 87--126.

Iterated function systems, Ruelle operators, and invariant projective measures
by Dorin E. Dutkay and Palle E. T. Jorgensen, Math. Comp. 75 (2006), 1931--1970.

Disintegration of projective measures
by Dorin E. Dutkay and Palle E. T. Jorgensen, Proc. Amer. Math. Soc., posted online June 22, 2006.

Certain representations of the Cuntz relations, and a question on wavelet decomposition
by Palle E. T. Jorgensen, accepted for Operator Theory, Operator Algebras, and Applications (Deguang Han, Palle Jorgensen, and David R. Larson, eds.), Contemp. Math., American Mathematical Society, Providence, to appear.

Use of operator algebras in the analysis of measures from wavelets and iterated function systems
by Palle E. T. Jorgensen, accepted for Operator Theory, Operator Algebras, and Applications (Deguang Han, Palle Jorgensen, and David R. Larson, eds.), Contemp. Math., American Mathematical Society, Providence, to appear.

Martingales, endomorphisms, and covariant systems of operators in Hilbert space
by Dorin E. Dutkay and Palle E. T. Jorgensen, J. Operator Theory, to appear (accepted November 2005, publication expected 2007).

Links to Other Publications

[Visibility!] Research Interests     

Non-Commutative Geometry

While widely cited, perhaps the term and the subject of "non-commutative geometry" are not really well defined: Each one of us is looking at non-commutative geometry within his/her own focus, and frame of reference. It is closely connected with the theory of operator algebras, e.g., Fundamentals of the Theory of Operator Algebras by Richard V. Kadison and John R. Ringrose. In many ways the subject is defined by Alain Connes's book Noncommutative Geometry. Connes's lovely book has the advantage that it covers "everything" if that is ever possible, and it presents the big picture, stressing connections between otherwise disparate areas of math and its applications, and it reveals a refreshing unity of mathematics. Many details are left to the reader to fill in. Occasionally I get the impression that Alain Connes tried to cover his life's work up to the time of his book, leaving out many proofs, or at least restricting the book to proof sketches. This also makes it difficult to point to some other more current book on non-commutative geometry that is some kind of modern supplement or alternative. In the Fall semester 2003, a math institute in Sweden, the Mittag-Leffler Institute is organizing a workshop around non-commutative geometry. It includes a variety of subjects, within a larger variety of possibilities: and there are Then of course, there are: My web site also gives some pointers to the literature on Since the subject of non-commutative geometry branches out so much, it is hard to say that one book covers it all. It is a vast subject, and each one of its many subdivisions could easily be the subject of books in its own right. Other books in math might refer to one aspect of non-commutative geometry, and yet not have an index entry for "non-commutative geometry". I think the difficulty there is that the various specializations do not actually agree on what the term "non-commutative geometry" covers. Another part of this web site includes additional relevant book reviews; see my reviews of math books on Amazon.

Mathematical Physics at the University of Iowa

Summary of Jorgensen's Research on Wavelets and Their Applications

Jorgensen's research involves several areas of mathematics and focuses on applications, spectral and tiling duality, and fractal iteration processes. The basic methods derive from operator algebras and representation theory, and the connection to the applications is threefold:

  1. Wavelet theory stands on the interface between signal processing and harmonic analysis. It concerns the mathematical tools involved in digitizing continuous data with view to storage, and the synthesis process, recreating the desired picture (or time signal) from the stored data. The algorithms involved go under the name of filter banks, and their spectacular efficiency derives in part from the use of (hidden) self-similarity in the data which is analyzed.
  2. Operators. Observations or time signals are functions, and classes of functions make up spaces. Numerical correlations add structure to the spaces at hand, Hilbert spaces. There are operators in the spaces deriving from the discrete data and others from the spaces of continuous signals. The first ones are good for computations, while the second reflect the real world. The operators between the two are the focus of Jorgensen's research.
  3. Relations between operations in the discrete and continuous domains. These relations are studied as symbols because symbols are programmable. The mathematics involved in assigning operators to the symbolic relations is called representation theory. The combination of the three areas opens up exciting new opportunities at the interface of mathematics and engineering. A main point is the study of intertwining operators between, on one side, the "discrete world" of high-pass/low-pass filters of signal processing, and on the other side, the "continuous world" of wavelets. There are significant operator-algebraic and representation-theoretic issues on both sides of the "divide", and the intertwining operators throw light on central issues for wavelets in higher dimensions.

    Tools from diverse areas of analysis, as well as from dynamical systems and operator algebra, merge into the research on wavelet analysis. The diversity of techniques is also a charm of the subject, which continues to generate new graduate student activity. Jorgensen had several recent students complete theses in the subject.

Some Wavelet Researchers

Links to Wavelet Web Pages

Links to Web Pages Covering Dynamics and Transfer Operators

Wavelets, Operators, etc., in the Popular Press

Broader Impact of Jorgensen's Research: Past, Present, and Future [PDF file]

My Reviews of Math Books on Amazon

Older Stuff: Research, Grants, Publications, Meetings, Activities, and Teaching

IFS with overlap

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been approved by the Division of Mathematical Sciences, the College of Liberal Arts or The University of Iowa.

Work displayed on this page was supported in part by the U.S. National Science Foundation under grants DMS-9987777, DMS-0139473(FRG), and DMS-0457581.

This page was last modified on 14 January 2007 by Brian Treadway.

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