Peter G. Casazza | Academic Influence

Peter G. Casazza's AcademicInfluence.com Rankings

Peter G. Casazza

Mathematics

#5320

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#7495

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Harmonic Analysis

#19

World Rank

#20

Historical Rank

Functional Analysis

#55

World Rank

#72

Historical Rank

Measure Theory

#2022

World Rank

#2452

Historical Rank

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Mathematics

Peter G. Casazza's Degrees

PhD Mathematics University of Missouri
Masters Mathematics University of Missouri
Bachelors Mathematics University of Missouri

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Why Is Peter G. Casazza Influential?

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According to Wikipedia, Peter G. Casazza, born June 28, 1945, in Albany, New York, is an American mathematician, presently working at the University of Missouri. He began his career as a Banach space theorist, but he is perhaps most well known for his role in the development of frame theory as a popular discipline of mathematical research.

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Peter G. Casazza's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

THE ART OF FRAME THEORY (1999) (594)
On signal reconstruction without phase (2006) (535)
Frames of subspaces (2003) (403)
Equal-Norm Tight Frames with Erasures (2003) (376)
Fusion frames and distributed processing (2006) (351)
On Tsirelson’s space (1984) (246)
Finite Frames: Theory and Applications (2012) (241)
Painless Reconstruction from Magnitudes of Frame Coefficients (2009) (201)
FRAMES FOR BANACH SPACES (1977) (190)
The Kadison–Singer Problem in mathematics and engineering (2005) (180)
Density, overcompleteness, and localization of frames (2006) (162)
Density, Overcompleteness, and Localization of Frames. I. Theory (2005) (151)
A Physical Interpretation of Tight Frames (2006) (115)
Phase retrieval (2015) (114)
FRAME EXPANSIONS IN SEPARABLE BANACH SPACES (2005) (113)
Density, Overcompleteness, and Localization of Frames. II. Gabor Systems (2005) (111)
Constructing tight fusion frames (2011) (103)
Deficits and Excesses of Frames (2003) (102)
Frames and the Feichtinger conjecture (2004) (93)
Chapter 7 - Approximation Properties (2001) (89)
Introduction to Finite Frame Theory (2013) (77)
Modern tools for weyl-heisenberg (gabor) frame theory (2001) (76)
Weaving Frames (2015) (76)
Weyl-Heisenberg frames for subspaces of L^2(R) (1998) (75)
The road to equal-norm Parseval frames (2010) (75)
Duality Principles in Frame Theory (2004) (74)
Banach spaces with a unique unconditional basis, up to permutation (1985) (70)
Phase retrieval in infinite-dimensional Hilbert spaces (2016) (68)
Robustness of Fusion Frames under Erasures of Subspaces and of Local Frame Vectors (2007) (67)
On symmetric basic sequences in Lorentz sequence spaces (1973) (66)
Weyl-Heisenberg frames, translation invariant systems and the Walnut representation (1999) (63)
FRAMES WITH A GIVEN FRAME OPERATOR (2002) (63)
Frames of translates (1998) (62)
Modeling sensor networks with fusion frames (2007) (62)
Minimizing Fusion Frame Potential (2009) (62)
Approximation of the Inverse Frame Operator and Applications to Gabor Frames (2000) (60)
Frames containing a Riesz basis and preservation of this property under perturbations (1995) (58)
Weaving properties of Hilbert space frames (2015) (58)
Weyl-Heisenberg frames for subspaces of ²() (2000) (57)
Phase Retrieval By Projections (2013) (57)
Optimally Sparse Frames (2010) (56)
Coefficient quantization for frames in Banach spaces (2007) (55)
Sparse fusion frames: existence and construction (2011) (54)
On signal reconstruction without noisy phase (2004) (53)
Auto-tuning unit norm frames (2010) (52)
A new identity for Parseval frames (2007) (51)
Geometry of Banach Spaces: Notes on approximation properties in separable Banach spaces (1991) (49)
Weaving Schauder frames (2015) (44)
A generalization of Gram–Schmidt orthogonalization generating all Parseval frames (2007) (43)
Roots of complex polynomials and Weyl-Heisenberg frame sets (2002) (42)
A quantitative notion of redundancy for finite frames (2009) (41)
Uniqueness of unconditional bases in Banach spaces (1996) (41)
A Gaussian average property of Banach spaces (1996) (40)
Frames for linear reconstruction without phase (2008) (39)
Sums of Hilbert space frames (2009) (39)
Perturbation of Regular Sampling in Shift-Invariant Spaces for Frames (2006) (38)
Equivalence of Reconstruction From the Absolute Value of the Frame Coefficients to a Sparse Representation Problem (2007) (37)
Fast algorithms for signal reconstruction without phase (2007) (37)
A brief introduction to Hilbert space frame theory and its applications (2015) (36)
Excesses of Gabor frames (2003) (36)
PROJECTIONS AND THE KADISON-SINGER PROBLEM (2007) (36)
Fourier Transforms of Finite Chirps (2006) (34)
Contemporary Mathematics Classes of Finite Equal Norm Parseval Frames (2008) (33)
Improved bounds in Weaver and Feichtinger conjectures (2015) (32)
Uniform Tight Frames with Erasures (2004) (32)
Every frame is a sum of three (but not two) orthonormal bases—and other frame representations (1998) (32)
Riesz-Fischer Sequences and Lower Frame Bounds (2002) (31)
The Paulsen Problem in Operator Theory (2011) (31)
The Reconstruction Property in Banach Spaces and a Perturbation Theorem (2008) (30)
Hilbert Space Frames Containing a Riesz Basis and Banach Spaces Which Have No Subspace Isomorphic toc0 (1995) (30)
Every Hilbert space frame has a Naimark complement (2011) (28)
Phase retrieval and norm retrieval (2014) (28)
Spectral Tetris Fusion Frame Constructions (2011) (28)
A Physical Interpretation for Finite Tight Frames (2003) (27)
Projections on Banach spaces with symmetric bases (1974) (27)
Unconditional bases and unconditional finite-dimensional decompositions in Banach spaces (1994) (26)
Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators (2010) (24)
On Some Classes of Primary Banach Spaces (1977) (24)
Decompositions of frames and a new frame identity (2005) (23)
BRACKET PRODUCTS FOR WEYL-HEISENBERG FRAMES (1999) (23)
Generalizing the Paley-Wiener perturbation theory for Banach spaces (1997) (23)
Self-induced compactness in Banach spaces (1994) (23)
A decomposition theorem for frames and the Feichtinger Conjecture (2007) (22)
A redundant version of the Rado–Horn Theorem (2006) (22)
Revisiting the Bourgain-Tzafriri restricted invertibility theorem (2009) (21)
On symmetric basic sequences in lorentz sequence spaces II (1974) (21)
Spanning and independence properties of frame partitions (2010) (21)
Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem (2014) (21)
Uniqueness of unconditional bases in c_0-products (1998) (20)
A General Construction of Spaces of the Type of R. C. James (1975) (20)
Norm Retrieval and Phase Retrieval by Projections (2017) (19)
Complex interpolation and complementably minimal spaces (1994) (18)
Classifying Tight Weyl-Heisenberg Frames (1998) (18)
On James’ quasi-reflexive Banach space (1977) (18)
Gabor Frames over Irregular Lattices (2003) (18)
Phase Retrieval Versus Phaseless Reconstruction (2015) (17)
EQUIVALENTS OF THE KADISON-SINGER PROBLEM (2006) (17)
James’ quasi-reflexive space is primary (1977) (17)
Fe b 20 06 THE KADISON-SINGER PROBLEM IN MATHEMATICS AND ENGINEERING : A DETAILED ACCOUNT (2008) (17)
Redundancy for localized frames (2011) (16)
OPERATORS AND FRAMES (2012) (15)
On signal reconstruction from absolute value of frame coefficients (2005) (15)
Necessary and sufficient conditions to perform Spectral Tetris (2012) (15)
Uniform tight frames for signal processing and communication (2001) (14)
Toward the classification of biangular harmonic frames (2016) (14)
PHASE RETRIEVAL BY VECTORS AND PROJECTIONS (2013) (14)
An example of an asymptotically Hilbertian space which fails the approximation property (2000) (14)
Constructions of biangular tight frames and their relationships with equiangular tight frames (2017) (12)
Local theory of frames and Schauder bases for Hilbert space (1998) (12)
The Maurey Extension Property for Banach Spaces with the Gordon-Lewis Property and related Structures (2003) (12)
Decompositions of Banach lattices into direct sums (1987) (11)
Some Questions Arising from the Homogeneous Banach Space Problem (1992) (11)
Gradient descent of the frame potential (2009) (11)
The Figiel-Johnson construction of Tsirelson's space (1989) (11)
The Kadison–Singer and Paulsen Problems in Finite Frame Theory (2013) (11)
Approximation of the frame coefficients using finite dimensional methods (1997) (10)
Frames and Schauder bases (1998) (10)
Analyzing the Weyl–Heisenberg Frame Identity (1999) (10)
FUSION FRAMES: EXISTENCE AND CONSTRUCTION (2009) (9)
Riesz frames and approximation of the frame coefficients (1998) (9)
Duality principles, localization of frames, and Gabor theory (2005) (9)
Frame Scalings: A Condition Number Approach (2015) (9)
On the rigidity of geometric and spectral properties of Grassmannian frames (2016) (9)
Weighted fusion frame construction via spectral tetris (2012) (9)
Some More Weak Hilbert Spaces (1998) (8)
Tight and random nonorthogonal fusion frames (2013) (8)
Characterizing Hilbert space frames with the subframe property (1997) (8)
A Banach space with a symmetric basis which is of weak cotype 2 but not of cotype 2 (2001) (8)
Perturbations of Weyl-Heisenberg frames (2000) (8)
Using projections for phase retrieval (2013) (8)
Fusion Frames and the Restricted Isometry Property (2011) (8)
Contemporary Mathematics Custom Building Finite Frames (2004) (8)
The Unconditional Constants for Hilbert Space Frame Expansions (2014) (8)
THE KNOWN EQUAL NORM PARSEVAL FRAMES AS OF 2005 (2005) (7)
The exact constant for the ℓ_1-ℓ_2 norm inequality (2017) (7)
Embeddings of Banach Spaces Into Banach Lattices and the Gordon–Lewis Property (1998) (7)
Finite dimensional decompositions in Banach spaces (1986) (7)
On the structures of Grassmannian frames (2017) (7)
Density Results for Frames of Exponentials (2006) (7)
Constructing fusion frames with desired parameters (2009) (6)
Infinite dimensional restricted invertibility (2009) (6)
An Introduction to Irregular Weyl-Heisenberg Frames (2004) (6)
Some geometric properties of Lorentz sequence spaces (1977) (6)
On a geometric condition related to boundedly complete bases and normal structure in Banach spaces (1972) (6)
Complemented ideals in the disk algebra (1980) (6)
On primary Banach spaces (1976) (5)
THE KADISON-SINGER PROBLEM AND THE UNCERTAINTY PRINCIPLE (2008) (5)
Chirps on finite cyclic groups (2005) (5)
Constructions and existence of tight fusion frames (2009) (5)
Projections of frames (2005) (5)
OPTIMALLY SPARSE FUSION FRAMES : EXISTENCE AND CONSTRUCTION (2010) (5)
THE BOURGAIN-TZAFRIRI CONJECTURE AND CONCRETE CONSTRUCTIONS OF NON-PAVABLE PROJECTIONS (2010) (5)
The Solution to the Frame Quantum Detection Problem (2017) (5)
CONSTRUCTING INFINITE TIGHT FRAMES (2005) (5)
Preserving injectivity under subgaussian mappings and its application to compressed sensing (2017) (5)
Fusion Frames and Unbiased Basic Sequences (2013) (4)
Perturbations and Irregular Sampling Theorems for Frames (2004) (4)
A fundamental identity for Parseval frames (2005) (4)
The Quantum Detection Problem: A Survey (2017) (4)
On the undefinability of Tsirelson's space and its descendants. (2018) (4)
Computing the Distance Between Frames and Between Subspaces of a Hilbert Space (2017) (4)
Physical laws governing finite tight frames (2003) (4)
Uniqueness of unconditional and symmetric structures in finite dimensional spaces (1990) (4)
CONSTRUCTION OF FINITE FRAMES WITH A GIVEN (2010) (4)
Phase retrieval by hyperplanes (2017) (4)
On uniqueness and plentitude of subsymmetric sequences (2021) (3)
The Fundamentals of Spectral Tetris Frame Constructions (2014) (3)
The paving conjecture is equivalent to the paving conjecture for triangular matrices (2007) (3)
Redundancy for localized and Gabor frames (2009) (3)
Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases (2018) (3)
On Nonreflexive Banach Spaces Which Contain No c 0 or l p (1980) (3)
A note on phase (norm) retrievable real Hilbert space fusion frames (2021) (3)
Remarks on Figiel's reflexive Banach spaces not isomorphic to their square (1978) (3)
Classifying characteristic functions giving Weyl-Heisenberg frames (2000) (3)
Weak phase retrieval and phaseless reconstruction (2016) (3)
Integer Frames (2013) (3)
Optimal Parseval frames: total coherence and total volume (2019) (2)
An elementary proof of a fundamental result in phase retrieval (2020) (2)
Riesz Outer Product Hilbert Space Frames: Quantitative Bounds, Topological Properties, and Full Geometric Characterization (2014) (2)
Controlled scaling of Hilbert space frames for R^2 (2020) (2)
Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators (2011) (2)
A FRAME THEORY PRIMER FOR THE KADISON-SINGER PROBLEM (2008) (2)
A DECOMPOSITION THEOREM FOR FRAMES AND THE WEAK FEICHTINGER CONJECTURE (2005) (2)
The simplified version of the Spielman and Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertiblity theorem (2012) (2)
A low complexity replacement scheme for erased frame coefficients (2009) (2)
Unconditional convergence constants of Hilbert space frame expansions (2015) (2)
A note on norm retrievable real Hilbert space frames (2022) (2)
Regular Two-Distance Sets (2019) (2)
Excess of Parseval frames (2005) (2)
Error Correction for Erasures of Quantized Frame Coefficients (2010) (2)
Block basic sequences in Tsirelson's space (1989) (2)
Upper and lower redundancy of finite frames (2010) (2)
A Notion of Optimal Packings of Subspaces with Mixed-Rank and Solutions (2019) (2)
A FRAME THEORY PRIMER FOR THE KADISON-SINGER PROBLEM (2008) (2)
An elementary, illustrative proof of the Rado-Horn Theorem (2011) (2)
The solution to the Maurey extension problem for Banach spaces with the Gordon-Lewis property and related structures (1999) (2)
CONCRETE CONSTRUCTIONS OF NON-PAVABLE PROJECTIONS (2010) (1)
Associating vectors in $\CC^n$ with rank 2 projections in $\RR^{2n}$: with applications (2017) (1)
THE JAMES FOREST (LMS Lecture Note Series 236) By H ELGA F ETTER and B ERTA G AMBOA de B UEN : 255 pp., £27.95 (LMS Members' price £20.96), ISBN 0 521 58760 3 (Cambridge University Press, 1997). (1999) (1)
What Are Mathematicians Really Like? Observations of a Spouse (2015) (1)
Piecewise scalable frames (2022) (1)
Variations on a Theme (1989) (1)
The Non-Definability of the Spaces of Tsirelson and Schlumprecht (2018) (1)
Modified Tsirelson's Space: T M (1989) (1)
Weak Phase Retrieval (2017) (1)
Permutations of the unit vector basis of Tsirelson's space (1989) (1)
Unconditional bases for complemented subspaces of Tsirelson's space (1989) (1)
The Naked Lecturer (2015) (1)
Spanning and Independence Properties of Finite Frames (2013) (1)
The Distributions of Hilbert Space Frame Vectors and Frame Coefficients (2015) (1)
Why I Became a Mathematician: A Personal Account (2015) (1)
Bounded linear operators on T and the “blocking” principle (1989) (1)
Subsequences of the unit vector basis of Tsirelson's space (1989) (1)
The infinite dimensional restricted invertibility theorem (2009) (1)
The Badly Taught High School Calculus Lesson and the Mathematical Journey It Led Me To (2015) (1)
Real phase retrieval by orthogonal complements and hyperplanes (2017) (1)
Non-orthogonal fusion frames (2011) (1)
Mathematicians and Mathematics (2015) (1)
Precursors of the Tsirelson construction (1989) (1)
Fundamental results on weak phase retrieval (2022) (1)
A tribute to Nigel J. Kalton (1946-2010) (2012) (1)
Perfectly Homogeneous Bases in Banach Spaces (1975) (1)
Operators and frames - Corrigendum (2017) (1)
Why I Became a Mathematician (2015) (0)
A Survey of Fusion Frames in Hilbert Spaces (2023) (0)
Spectral Tetris Fusion Frame Constructions (2012) (0)
PROBLEMS ON PAVING AND THE KADISON-SINGER PROBLEM (2008) (0)
The Psychology of Being a Mathematician (2015) (0)
We Are Different (2015) (0)
The commuting B.A.P. for Banach spaces (1989) (0)
Some final comments (1989) (0)
A Mathematician's Eye View (2015) (0)
Foreword to Who Are Mathematicians (2015) (0)
Chapter 1 Introduction to Finite Frame Theory (2019) (0)
FA ] 2 2 A ug 2 00 0 Classifying Characteristic functions giving Weyl-Heisenberg Frames (2000) (0)
F A ] 14 O ct 1 99 9 The solution to the Maurey extension problem for Banach spaces with the Gordon-Lewis property and related structures (1999) (0)
GABOR SYSTEMS (0)
Why I am a Mathematician (2015) (0)
Foreword to On Becoming a Mathematician (2015) (0)
Foreword to Why I Became a Mathematician (2015) (0)
1 An Introduction to Irregular Weyl-Heisenberg Frames (2006) (0)
Genus $n$ Banach spaces (1998) (0)
Geometric and Spectral Properties of Grassmannian Frames in $\mathbb C^2$ (2016) (0)
Phase retrieval by projections in R^n requires 2n-2 projections (This paper has a gap) (2020) (0)
I am a Mathematician (2015) (0)
Chapter 1 Fusion Frames (2012) (0)
CONTROLED SCALING OF HILBERT SPACE FRAMES FOR R2 (2020) (0)
Singular integrals, BMO, Hp (1984) (0)
Dynamics of Mathematical Groups (2015) (0)
New characterizations of the unit vector basis of or (2023) (0)
Frames from first principles : Error correction , symmetry goals , and numerical efficiency (2009) (0)
Chapter 1 Spanning and Independence Properties of Finite Frames (2012) (0)
FA ] 1 4 A pr 2 01 0 SPANNING AND INDEPENDENCE PROPERTIES OF FRAME PARTITIONS (2021) (0)
PAVING AND THE KADISON-SINGER PROBLEM (0)
Book Review: Classical sequences in Banach spaces (1994) (0)
When are frames close to equal-norm Parseval frames? (2009) (0)
Auto-tuning Unit Norm Frames Auto-tuning Unit Norm Frames (2020) (0)
The Core of a Grassmannian Frame (2022) (0)
What's a Nice Guy Like Me Doing in a Place Like This? (2015) (0)
New characterizations of the unit vector basis of $c_0$ or $\ell_p$ (2022) (0)
Applied Mathematics (2019) (0)
A QUANTITATIVE NOTION OF REDUNDANCY AND ITS APPLICATIONS (2011) (0)
FRAMES AND THE KADISON-SINGER PROBLEM : A REPORT FOR AIM (2008) (0)
Questions about Mathematics (2015) (0)
Weighted fusion frame construction via spectral tetris (2013) (0)
FRAMES AND THE KADISON-SINGER PROBLEM (0)
FUSION FRAMES AND THEORETICAL APPLICATIONS: FOR THE FUSION FRAME WEB PAGE (2008) (0)
Social Class and Mathematical Values in the USA (2015) (0)
The distance between frames and betweensubspaces of a Hilbert space (2016) (0)
Partitioning Hadamard vectors into Hadamard matrices (2016) (0)
The unconditional constants of frame expansions and cross-frame expansions (2015) (0)
Real matrices whose columns have equal modulus coordinates (2023) (0)
ON THE KADISON-SINGER CONJECTURE FOR THE ARCC MEETING (2006) (0)
4.1. Complemented subspaces of A, H1, and H∞ (1984) (0)
The Solution to the Frame Quantum Detection Problem (2018) (0)
Index of volume 43 (2000) (0)
Embedding Theorems about T and T (1989) (0)
Bases equivalent to the unit vector basis of $c_0$ or $\ell_p$ (2022) (0)
Remarks on scalable frames (2022) (0)
m at h . FA ] 1 4 A pr 1 99 8 GENUS N BANACH SPACES (1998) (0)
DECOMPOSITIONS OF BANACH LATTICES 779 { PXlly } j ° ° l (2009) (0)
Sparse recovery using the preservability of the null space property under random measurements (2017) (0)
Isomorphisms between subspaces of Tsirelson's space which are spanned by subsequences of \(\left\{ {t_n } \right\}_{n = 1}^\infty\) (1989) (0)
A note on (weak) phase and norm retrievable Real Hilbert space frames and projections (2021) (0)
Frames in Compressive Sensing and Approximate Signal Recovery Pertaining to Physical Sensing Matrices (2014) (0)
J ul 2 01 7 TOWARD THE CLASSIFICATION OF BIANGULAR HARMONIC FRAMES (2017) (0)
Phase Retrieval in $\ell_2(\RR)$ (2018) (0)
Regular Two-Distance Sets (2020) (0)
Preface (2012) (0)
Beyond Kadison-Singer: paving and consequences (2019) (0)
The Norms of Projections Onto Ideals in the Disk Algebra (1992) (0)
Mathematics (2019) (0)
Analysis in functional spaces (1984) (0)
Classifying weak phase retrieval (2023) (0)
N ov 1 99 9 ANALYZING THE WEYL-HEISENBERG FRAME IDENTITY (2008) (0)

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