John J. Benedetto
Department of Mathematics
University of Maryland
College Park, MD 20742
Office: Room 3104 (Math Building)
Office Phone: Main: 301-405-5175 Alt: 301-405-5161
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 editor-in-chief.
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, Der-Chen 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
Click here for Harmonic Analysis lecture for graduate students (2002).
Click here for Finite Frames with Applications to Sigma-Delta Quantization and MRI lecture with Matt Fickus, Stuart Fletcher, Alfredo Nava-Tudela, 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 Sigma-Delta 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 non-linear frame theoretic problems
Click here for some of the beautiful people associated with the following theses, as well as other mathematician friends.
|1||George Benke||Sidon sets and the growth of Lp norms||1971|
|2||Wan-chen Hsieh||Topologies for spectral synthesis of the space of bounded functions||1977|
|3||Fulvio Ricci||Support preserving multiplication of pseudo-measures||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||Jean-Pierre Gabardo||Spectral gaps and uniqueness problems in Fourier analysis||1987|
|-||--||Sloan Dissertation Fellowship||1986|
|7||David Walnut||Weyl-Heisenberg 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 Wiener-Wintner theorem in higher dimensions||1990|
|10||George Yang||Applications of Wiener-Tauberian 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||Hui-Chuan 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||Sigma-Delta 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, product-convolution operators, and the tensor product of frames||2006|
|35||Aram Tangboondouangjit||Sigma-Delta 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, co-advisor)||2008|
|39||Emily King||Wavelet and Frame Theory: Frame Bound Gaps, Generalized Shearlets, Grassmannian Fusion Frames and p-adic Wavelets (Wojciech Czaja, co-advisor)||2009|
|40||Matthew Hirn||Enumeration of Harmonic Frames and Frame Based Dimension Reduction (Kasso Okoudjou, co-advisor)||2009|
|41||Justin Christopher Flake||The multiplicative Zak transform, dimension reduction, and wavelet analysis of LIDAR data (Wojciech Czaja, co-advisor)||2010|
|42||Enrico Au-Yeung||Balayage of Fourier transforms and the theory of frames||2011|
|43||Avner Halevy||Extensions of Laplacian Eigenmaps for Manifold Learning (Wojciech Czaja, co-advisor)||2011|
|44||Nathaniel Strawn||Geometric structures and optimization on finite frames (Radu Balan, co-advisor)||2011|
|45||Alfredo Nava-Tudela||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, co-advisor)||2013|
|48||Travis Andrews||Frame Multiplication Theory for Vector-valued Harmonic Analysis||2014|
|49||Alex Cloninger||Exploiting Data-Dependent Structure for Improving Sensor Acquisition and Integration (Wojciech Czaja, co-advisor)||2014|
|50||Tim Doster||Harmonic Analysis Inspired Data Fusion for Applications in Remote Sensing (Wojciech Czaja, co-advisor)||2014|
|51||Wei-Hsuan Yu||Spherical Two-Distance Sets and Related Topics in Harmonic Analysis (Alexander Barg, co-advisor)||2014|
|52||James Murphy||Anisotropic Harmonic Analysis and Integration of Remotely Sensed Data (Wojciech Czaja, co-advisor)||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, co-advisor)||2016|
|56||Mark Magsino||Constant amplitude zero-autocorrelation sequences and single pixel camera imaging||2018|
|57||Weilin Li||Topics on harmonic analysis, sparse representations, and data analysis (Wojciech Czaja, co-advisor)||2018|
|58||Franck Olivier Ndjakou Njeunje||Computational Methods in Machine Learning: Transport Model, Haar Wavelet, DNA Classification, and MRI (Wojciech Czaja, co-advisor)||2018|
|59||Shujie Kang||TBA (Kasso Okoudjou, co-advisor)||2019|
|64||Christiana Sabett||TBA (Alfredo Nava-Tudela, co-advisor)||2020|
|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||Rong-Song Jih||Some characteristics of R-synthesizable 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 Nava-Tudela||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||Wei-Hsuan 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 multi-dimensional narrow band ambiguity function||2012|
|32||Tim Doster||Non-linear dimension reduction||2012|
|33||Christian Sykes||Wavelet auditory modeling||2013|
|34||James Murphy||Continuous frames and co-orbit spaces||2013|
|35||Christiana Sabett||Finite Frames for MRI computation||2016|
|36||Sandeep Yaddula||The Hilbert transform and applications||2016|
|37||Raymond Schram||Sigma-Delta Quantization||2018|
Here are some other connections: