Professor CV (2 pg.) CV (5 pg.)
Office  Paper Mail  Phone  

25B  jorgen@math.uiowa.edu 
Palle Jorgensen Department of Mathematics 14 MLH The University of Iowa Iowa City, IA 522421419 USA 
voice: 3193350782 fax: 3193350627 
22M:210 (Fall 2007)
22M:313 (Fall 2007)
Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanicsby Palle E. T. Jorgensen 
Analysis and Probability:

Wavelets through a Looking Glass: The World of the Spectrumby Ola Bratteli and Palle E. T. JorgensenApplied and Numerical Harmonic Analysis, Birkhäuser, 2002 
Excerpts [PDF files]:
Prerelease announcements:
CAMDigest
The Wavelet Digest
Books on wavelets
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]
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
Wavelets with fixed support are
known to vary with parameters,
and they can be viewed in motion in
A flipbook of wavelets on the interval [0,5] and their associated scaling functions [large PDF file]. 
Compare Wim Sweldens's Wavelet Cascade Applet  Twoparameter family of compactly supported wavelets 
About the Book Cover, the Dedication, and Yosemite 
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
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):340363, 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 KarhunenLoeve Transforms," Acta Appli candae Mathematica, 108, 5:498508, 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.
Spectral Theory for Discrete Lapacians
by Dorin E. Dutkay and Palle E. T. Jorgensen,
, submitted.
Essential selfadjointness of the graphLaplacian
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 2:449478, 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
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 MyungSin 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), 181222.
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 BaumslagSolitar 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), 217238.
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 KarhunenLoeve Transforms
by Palle E. T. Jorgensen and MyungSin Song,
J. Math. Phys. 48 no. 10 (2007), 103503.
KadisonSinger 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).
KadisonSinger 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 0387295194.
Wavelets on fractals
by Dorin E. Dutkay and Palle E. T. Jorgensen,
Rev. Mat. Iberoamericana 22 (2006), 131180.
Oversampling generates superwavelets
by Dorin E. Dutkay and Palle E. T. Jorgensen,
Proc. Amer. Math. Soc., to appear.
A nonMRA C^{r}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), 251270.
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 nonlinear 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. 87126.
Iterated function systems, Ruelle operators, and invariant projective measures
by Dorin E. Dutkay and Palle E. T. Jorgensen,
Math. Comp. 75 (2006), 19311970.
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).
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:
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.
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 DMS9987777, DMS0139473(FRG), and DMS0457581.
This page was last modified on 14 January 2007 by Brian Treadway.