John J. Benedetto
Professor
Department of Mathematics
University of Maryland
College Park, MD 20742
Office: Room 3104 (Math Building)
Office Phone: Main: 3014055175 Alt: 3014055161
email: jjb@math.umd.edu
Wikipedia
I received my BA from Boston College in 1960, my MA from Harvard University in 1962, and my Ph.D. from the University of Toronto in 1964 under the direction of Chandler Davis [Personal Site] [Wikipedia]. Chandler received his Ph.D. from Harvard University in 1950 under the direction of Garrett Birkhoff [Wikipedia], who was a member of Harvard's Society of Fellows and did not have a Ph.D. In 2014 I contributed to an article entitled "Chandler Davis as Mentor" which appeared in The Mathematical Intelligencer, of which Chandler was an editorinchief.
Click here for speakers and photos from the Conference on Harmonic Analysis and Applications. The Department of Mathematics at University of Maryland sponsored the Conference, and its organizers were George Benke, DerChen Chang, Chris Heil, Raymond Johnson, and David Walnut. Click here for photos documenting some nocturnal activities associated with the Conference.
Page 1 of Harmonic Analysis,
by John J. Benedetto.
Page 2 of Harmonic Analysis (Sampling and Frames),
by John J. Benedetto.
Math 634: Harmonic Analysis .
Click here for course syllabus.
Math 858W: Selected Topics in Analysis; Frames, Sampling, and Wavelets.
Click here for course syllabus.
Trivia from an old office:
Board 1, Board 2, Board 3, Board 4, Board 5
Office door
Click here for Harmonic Analysis
lecture for graduate students (2002).
Click here for Finite Frames with
Applications to SigmaDelta Quantization and MRI lecture
with Matt Fickus, Stuart Fletcher, Alfredo NavaTudela,
Alex Powell, Yang B. Wang, and Ozgur Yilmaz (2004).
Click here for Quantum Detection and
Finite Frames lecture
with Andrew Kebo (2005).
Click here for
Waveform Design and Quantum Detection Matched Filtering lecture (2005).
Click here for
Waveform Design and SigmaDelta Quantization lecture (2006).
Click here for
Notes from the Math 648 course, Wavelet Theory and Applications.
Click here for Lecture notes from the 2008 Math 648 course, Wavelet Theory and Applications
Click here for Video
of Math 648 course in Wavelet theory (Fall 2008)
Click here for Lecture slides from the Illinois/Missouri Applied
Harmonic Analysis Seminar (March 2009).
Click here for a video of a lecture from "Frames from first principles:
Error correction, symmetry goals, and numerical efficiency" at the Banff
research station in March 2009: Some
nonlinear frame theoretic problems
Click here for some of the beautiful people associated with the following theses, as well as other mathematician friends.
Student  Thesis title  Year  

1  George Benke  Sidon sets and the growth of L^{p} norms  1971 
2  Wanchen Hsieh  Topologies for spectral synthesis of the space of bounded functions  1977 
3  Fulvio Ricci  Support preserving multiplication of pseudomeasures  1977 
4  Ward Evans  Beurling's spectral analysis and continuous pseudomeasues  1980 
5  W. David Joyner  The harmonic analysis of Dirichlet series and the Riemann zeta function  1983 
    NSF Post Doc IAS  1984 
6  JeanPierre Gabardo  Spectral gaps and uniqueness problems in Fourier analysis  1987 
    Sloan Dissertation Fellowship  1986 
7  David Walnut  WeylHeisenberg wavelet expansions: existence and stability in weighted spaces  1989 
    Sloan Dissertation Fellowship  1988 
8  Christopher Heil  Wiener amalgam spaces in generalized harmonic analysis and wavelet theory  1990 
    NSF Post Doc MIT  1990 
9  Rodney Kerby  Correlation function and the WienerWintner theorem in higher dimensions  1990 
10  George Yang  Applications of WienerTauberian theorem to a filtering problem and convolution equations  1990 
11  William Heller  Frames of exponentials and applications  1991 
12  Joseph Lakey  Weighted norm inequalities for the Fourier transform  1991 
13  Erica Bernstein  Generalized Riesz products and pyramidal schemes  1992 
14  Anthony Teolis  Discrete signal representation  1993 
15  Shidong Li  The theory of frames and filter design  1993 
16  Sandra Saliani  Nonlinear wavelet packets  1993 
17  Georg Zimmermann  Projective multiresolution analysis and generalized sampling  1994 
18  Melissa Lynn Harrison  Frames and irregular sampling from a computational perspective  1998 
19  HuiChuan Wu  Multidimensional irregular sampling in terms of frames  1998 
20  Manuel T. Leon  Minimally supported frequency wavelets  1999 
21  Goetz E. Pfander  Periodic wavelet transforms and periodicity detection  1999 
22  Oliver Mike Treiber  Affine data representations and filter banks  1999 
23  Sherry Scott  Spectral analysis of fractal noise in terms of Wiener's Generalized Harmonic Analysis and wavelet theory  2000 
24  Matthew Fickus  Finite normalized tight frames and spherical equidistribution  2001 
25  Ioannis Konstantinidis  The characterization of multiscale generalized Riesz product measures  2001 
26  Songkiat Sumetkijakan  A fractal set constructed from a class of wavelet sets  2002 
27  Anwar A. Saleh  A finite dimensional model for the inverse frame operator  2002 
28  Jeffrey Sieracki  Greedy adaptive discrimination: signal component analysis by simultaneous matching pursuit with application to ECoG signature detection  2002 
29  Alex Powell  The uncertainty principle in harmonic analysis and Bourgain's theorem  2003 
30  Shijun Zheng  Besov spaces for the Schrodinger operator with barrier potential  2003 
31  Joseph Kolesar  SigmaDelta modulation and correlation criteria for the construction of finite frames arising in communication theory  2004 
32  Andrew Kebo  Quantum detection and finite frames  2005 
33  Juan Romero  Generalized multiresolution analysis: construction and measure theoretic characterization  2005 
34  Abdelkrim Bourouihiya  Beurling weighted spaces, productconvolution operators, and the tensor product of frames  2006 
35  Aram Tangboondouangjit  SigmaDelta quantization: Number theoretic aspects of refining quantization error  2006 
36  Somantika Datta  Wiener's Generalized Harmonic Analysis and waveform design  2007 
37  Onur Oktay  Frame quantization theory and equiangular tight frames  2007 
38  David Widemann  Dimensionality reduction for hyperspectral data (Wojciech Czaja, coadvisor)  2008 
39  Emily King  Wavelet and Frame Theory: Frame Bound Gaps, Generalized Shearlets, Grassmannian Fusion Frames and padic Wavelets (Wojciech Czaja, coadvisor)  2009 
40  Matthew Hirn  Enumeration of Harmonic Frames and Frame Based Dimension Reduction (Kasso Okoudjou, coadvisor)  2009 
41  Justin Christopher Flake  The multiplicative Zak transform, dimension reduction, and wavelet analysis of LIDAR data (Wojciech Czaja, coadvisor)  2010 
42  Enrico AuYeung  Balayage of Fourier transforms and the theory of frames  2011 
43  Avner Halevy  Extensions of Laplacian Eigenmaps for Manifold Learning (Wojciech Czaja, coadvisor)  2011 
44  Nathaniel Strawn  Geometric structures and optimization on finite frames (Radu Balan, coadvisor)  2011 
45  Alfredo NavaTudela  Image Representation and Compression via Sparse Solutions of Systems of Linear Equations  2012 
46  Kevin Duke  A Study of the Relationship between Spectrum and Geometry through Fourier Frames and Laplacian Eigenmaps  2012 
47  Rongrong Wang  Global geometric conditions on sensing matrices for the success of L1 minimization algorithm (Wojciech Czaja, coadvisor)  2013 
48  Travis Andrews  Frame Multiplication Theory for Vectorvalued Harmonic Analysis  2014 
49  Alex Cloninger  Exploiting DataDependent Structure for Improving Sensor Acquisition and Integration (Wojciech Czaja, coadvisor)  2014 


50  Tim Doster  Harmonic Analysis Inspired Data Fusion for Applications in Remote Sensing (Wojciech Czaja, coadvisor)  2014 
51  WeiHsuan Yu  Spherical TwoDistance Sets and Related Topics in Harmonic Analysis (Alexander Barg, coadvisor)  2014 
52  James Murphy  Anisotropic Harmonic Analysis and Integration of Remotely Sensed Data (Wojciech Czaja, coadvisor)  2015 
53  Paul Koprowski  Finite Frames and Graph Theoretic Uncertainty Principles  2015 
54  Gokhan Civan  Identification of Operators on Elementary Locally Compact Abelian Groups  2015 
55  Matthew Begué  Expedition in Data and Harmonic Analysis on Graphs (Kasso Okoudjou, coadvisor)  2016 
56  Mark Magsino  Constant amplitude zeroautocorrelation sequences and single pixel camera imaging  2018 
57  Weilin Li  Topics on harmonic analysis, sparse representations, and data analysis (Wojciech Czaja, coadvisor)  2018 


58  Christiana Sabett  TBA (Alfredo NavaTudela, coadvisor)  2018 
59  Franck Olivier Ndjakou Njeunje  TBA (Wojciech Czaja, coadvisor)  2018 
60  Shujie Kang  TBA (Kasso Okoudjou, coadvisor)  2019 
61  KungChing Lin  TBA  2019 
62  Chenzhi Zhao  TBA  2019 
63  Ryan Cinoman  TBA  2020 
64  Raymond Schram  TBA  2020 
Student  Thesis title  Year  

1  Joanne Costello  Integration theory  1969 
2  Pamela Rowe  The uncertainty principle  1980 
3  David Kirk  The ambiguity function and the Wigner Distribution  1984 
4  John Montroll  AM and FM  1984 
5  Lonnie Carey  Maximum entropy and the moment problem  1985 
6  RongSong Jih  Some characteristics of Rsynthesizable closed subalgebras of l^p  1985 
7  David Scott  Prolate spheroidal wave functions and the uncertainty principle in signal analysis  1986 
8  Rodney Kerby  Correlation functions and applications  1988 
9  Erica Bernstein  Carleson's Theorem  1990 
10  Michael Hernandez  Disjointness results for some classes of stable stochastic processes (for Christian Houdre')  1992 
11  Paul Miller  Nonseparable multidimensional filter banks  1993 
12  Glenn Easley  Frames, sampling, and reconstruction algorithms  1996 
13  Goetz Pfander  Wavelet detection of periodic behavior in EEG and ECoG data  1998 
14  Oliver Treiber  Affine frames and shift invariant systems in L^2(R^d)  1998 
15  Katharine Feehan  Wavelets in finance: Comparative study of nonparametric techniques for fitting the yield curve in the commercial paper market  1999 
16  Alfredo NavaTudela  Signal processing for health monitoring of jet engines  1999 
17  Alex Powell  Quadrature mirror filters  1999 
18  Andrew Kebo  Quantum detection and geometrically uniform frames  2004 
19  Richard Hallquist  The Dieudonne'Grothendieck theorem  2004 
20  Ming Wei Ong  Maximum entropy and the extension problem for positive definite distributions  2004 
21  Abdelkrim Bourouihiya  Multipliers of Beurling algebras  2004 
22  Onur Oktay  Maximum entropy and the extension problem for positive definite distributions  2005 
23  Justin Christopher Flake  Factorization of group algebras  2006 
24  Leon Escobar  MAIT Masters program  2008 
25  Kenneth MacDonald  Barker Sequences, Theory and Applications  2009 
26  Joseph Misiti  MAIT Masters program  2010 
27  Jae Hyup Hong  Fusion frames and applications  2010 
28  WeiHsuan Yu  Minimizing fusion frame potential  2010 
29  Kevin Hencke  Using a discriminator to improve compressive sensing efficiency  2012 
30  Paul Koprowski  Uncertainty Principles of the Fourier Transform  2012 
31  Benjamin Lauser  A multidimensional narrow band ambiguity function  2012 
32  Tim Doster  Nonlinear dimension reduction  2012 
33  Christian Sykes  Wavelet auditory modeling  2013 
34  James Murphy  Continuous frames and coorbit spaces  2013 
35  Christiana Sabett  Finite Frames for MRI computation  2016 
36  Sandeep Yaddula  The Hilbert transform and applications  2016 
37  Raymond Schram  SigmaDelta Quantization  2018 
Here are some other connections: