John J. Benedetto

Department of Mathematics, University of Maryland

John J. Benedetto
Professor
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
email: jjb@math.umd.edu
Wikipedia

Director of The Norbert Wiener Center for Harmonic Analysis and Applications
Series editor of the Applied and Numerical Harmonic Analysis book series,
published by Birkhauser
Executive editor and founding editor-in-chief of the Journal of Fourier Analysis and Applications,
published by Birkhauser
PhD Students (see below)
MA Students (see below)
Books (see below)
Some preprints since 2000 (and a few older ones)
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 1999 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.

2019 Jubilee of Fourier Analysis and Applications: A Conference Celebrating John Benedetto's 80th Birthday
Article on the Jubilee
Select talks from the Jubilee:
The 1960s - Some people and mathematics I met, John Benedetto

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

Harmonic Analysis lecture for graduate students (2002).
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).
Quantum Detection and Finite Frames lecture with Andrew Kebo (2005).
Waveform Design and Quantum Detection Matched Filtering lecture (2005).
Waveform Design and Sigma-Delta Quantization lecture (2006).
Notes from the Math 648 course, Wavelet Theory and Applications.
Lecture notes from the 2008 Math 648 course, Wavelet Theory and Applications
Video of Math 648 course in Wavelet theory (Fall 2008)
Lecture slides from the Illinois/Missouri Applied Harmonic Analysis Seminar (March 2009).
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
CodEx 2020 online seminar: Spectral super-resolution and unique extensions for complex measures CodEx site
Pescosansonesco
John B. Benedetto
Robert L. Benedetto
Gary L. Benedetto
Karen Grace Benedetto
Amy Elise Benedetto
Lucas Campion Benedetto
Mark Jamison Benedetto
Mia Elizabeth Benedetto
Lily Joanna Benedetto
Ariana Catherine Benedetto
Eulogy for Dan Sweet
Eulogy for Fred Williams
Other Connections (see below)
Click here for some of the beautiful people associated with the following theses, as well as other mathematician friends.

PhD Students

	Student	Thesis title	Year
1	George Benke	Sidon sets and the growth of L^p 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 pseudomeasures	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
--	--	Ann G. Wylie Dissertation Fellow
39	Emily King	Wavelet and Frame Theory: Frame Bound Gaps, Generalized Shearlets, Grassmannian Fusion Frames and p-adic Wavelets (Wojciech Czaja, co-advisor)	2009
--	--	NIH Postbac IRTA, Humboldt Research Fellow
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
--	--	Ann G. Wylie Dissertation Fellow
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
--	--	Ann G. Wylie Dissertation Fellow
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	Generalized Frame Potential and Problems Related to SIC-POVMs (Kasso Okoudjou, co-advisor)	2019
60	Kung-Ching Lin	Nonlinear Sampling Theory and Efficient Signal Recovery	2019
61	Chenzhi Zhao	Applications of Nonharmonic Fourier Analysis and Single Pixel Camera Design	2019
62	Ryan Cinoman	Uniqueness for continuous superresolution by means of Choquet theory and geometric measure theory	2020
63	Raymond Schram	Topics in Harmonic Analysis: The HRT Conjecture and Sigma Delta Quantization	2020

MA students

	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	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	2019

Books

Generalized Functions, Institute for Fluid Dynamics and Applied Math., BN-431 (1966) 1-380.
Harmonic Analysis on Totally Disconnected Sets, Lecture Notes in Mathematics, 202, Springer-Verlag, NY, 1971.
Spectral Synthesis, Pure and applied mathematics series, 66, Academic Press, NY, 1975.
Real Variable and Integration with Historical Notes, Math. Leitfaden series, Teubner, Stuttgart, 1976.
(Editor) Euclidean Harmonic Analysis, Lecture Notes in Mathematics 779, Springer-Verlag, NY, 1979.
(Editor, with M.W. Frazier) Wavelets: Mathematics and Applications, CRC Press, Boca Raton, FL, 1994.
(Also translated into Japanese, published by Springer-Verlag, NY, 1995)
Harmonic Analysis and Applications, CRC Press, Boca Raton, FL, 1997.
(Editor, with P.J.S.G. Ferreira) Modern Sampling Theory: Mathematics and Applications, Applied and Numerical Harmonic Analysis Series, Birkhauser, Boston, MA, 2001.
(Editor, with A. Zayed) Sampling, Wavelets, and Tomography, Applied and Numerical Harmonic Analysis Series, Birkhauser, Boston, MA, 2004.
(with W. Czaja) Integration and Modern Analysis: from Classical Real Variables to Distribution Theory, Birkhauser, Boston, MA, 2009.
(Editor, with T. Andrews, R. Balan, W. Czaja, and K. Okoudjou) of Excursions in Harmonic Analysis, the February Fourier Talks (FFT) at the Norbert Wiener Center, Volume 1, Springer-Birkauser, New York, 2013.
(Editor, with T. Andrews, R. Balan, W. Czaja, and K. Okoudjou) of Excursions in Harmonic Analysis, the February Fourier Talks (FFT) at the Norbert Wiener Center, Volume 2, Springer-Birkauser, New York, 2013.
(Editor, with T. Andrews, R. Balan, W. Czaja, and K. Okoudjou) of Excursions in Harmonic Analysis, the February Fourier Talks (FFT) at the Norbert Wiener Center, Volume 3, Springer-Birkauser, New York, 2013.
(Editor, with T. Andrews, R. Balan, W. Czaja, and K. Okoudjou) of Excursions in Harmonic Analysis, the February Fourier Talks (FFT) at the Norbert Wiener Center, Volume 4, Springer-Birkauser, New York, 2013.
(Editor, with T. Andrews, R. Balan, W. Czaja, and K. Okoudjou) of Excursions in Harmonic Analysis, the February Fourier Talks (FFT) at the Norbert Wiener Center, Volume 5, Springer-Birkauser, New York, 2013.

Publications

Representation theorem for the Fourier transform of integrable functions, Bull. Soc. Roy. Sci. de Liege 9-10 (1965), 601-604.
Onto Criterion for adjoint maps, Bull. Soc. Roy. Sci. de Liege 9-10 (1965), 605-609.
The Laplace transform of generalized functions, Canad. J. Math. 18 (1966), 357-374.
Tauberian translation algebras, Ann. di Mat. 74 (1967), 255-282.
Analytic representation of generalized functions, Math .Zeit. 97 (1967), 303-319.
A strong form of spectral resolution, Ann. di Mat. 86 (1970), 313-324.
Sets without true distributions, Bull. Soc. Roy. Sci. de Liege 7-8 (1970), 434-437.
Support preserving measure algebras and spectral synthesis, Math. Zeit. 118 (1970), 271-280.
Trigonometric sums associated with pseudo-measures, Ann. Scuola Norm. Sup., Pisa 25 (1971), 229-248.
Sui problemi di sintesi spettrale, Rend. Sem. Mat., Milano 4l (1971), 55-61.
Il Problema degli insiemi Helson-S, Rend. Sem. Mat., Milano 41 (1971), 63-68.
(LF) spaces and distributions on compact groups and spectral synthesis on R/Z; Math. Ann. 194 (1971), 52-67.
Ensembles de Helson et synthese spectrale, CRAS, Paris 274 (1972), 169-170.
Construction de fonctionnelles multiplicatives discontinues sur des algebres metriques, CRAS, Paris 274 (1972), 254-256.
A support preserving Hahn-Banach property to determine Helson-S Sets, Inventiones Math. 16 (1972), 214-228.
Idele characters in spectral synthesis on R/Z; Ann. Inst. Fourier 23 (1973), 45-64.
Pseudo-measure energy and spectral synthesis, Can. J. Math. 26 (1974), 985-1001.
Tauberian theorems, Wiener's spectrum, and spectral synthesis, Rend. Sem. Mat., Milano 44 (1974), 63-73.
The Wiener spectrum in spectral synthesis, Studies in Applied Math. (MIT) 54 (1975), 91-115.
Idelic pseudo-measures and Dirichlet series, Symposia Mathematica, Academic Press, 1976 Conference on Harmonic Analysis, Rome 22 (1977), 205-222.
Zeta Functions for idelic pseudo-measures, Ann. Scuola Norm. Sup., Pisa 6 (1979) 367-377.
Fourier analysis of Riemann distributions and explicit formulas, Math. Ann. 252 (1980), 141-164.
The theory of constructive signal analysis, Studies in Applied Math. (MIT) 65 (1981), 37-80.
A closure problem for signals in semigroup invariant systems, SIAM J. Math. Analysis 13 (1982),180-207.
Harmonic analysis and spectral estimation, J. Math. Analysis and Applications 91 (1983), 444-509.
(With H. Heinig) Weighted Hardy spaces and the Laplace transform, Lecture Notes in Mathematics, 992, Springer Verlag (Cortona Conference, 1982), (1983), 240-277.
Wiener's Tauberian theorem and the uncertainty principle, Proc. of Modern Harmonic Analysis Conference, Torino-Milano (1982), (1983), 863-887.
A local uncertainty principle, SIAM, J. Math. Analysis 15 (1984), 988-995.
An inequality associated with the uncertainty principle, Rend. Circ. Mat. di Palermo 34 (1985), 407-421.
Some mathematical methods for spectrum estimation, in Fourier Techniques and Applications, J.F. Price, editor, Plenum Publishing (1985), 73-100.
Fourier uniqueness criteria and spectrum estimation theorems, in Fourier Techniques and Applications, J.F. Price, editor, Plenum Publishing (1985), 149-172.
Inequalities for spectrum estimation, Linear Algebra and Applications 84 (1986), 377-383.

Here are some other connections: