Hardcover ISBN:  9781470420192 
Product Code:  PSAPM/73 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
Electronic ISBN:  9781470432126 
Product Code:  PSAPM/73.E 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 

Book DetailsProceedings of Symposia in Applied MathematicsVolume: 73; 2016; 264 ppMSC: Primary 15; 41; 42; 47; 52; 65; 90;
Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics.
This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX.
Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents stateoftheart results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the nonexpert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.ReadershipGraduate students and research mathematicians interested in frame theory and its applications.

Table of Contents

Articles

Peter G. Casazza and Richard G. Lynch  A Brief Introduction to Hilbert Space Frame Theory and its Applications

Dustin G. Mixon  Unit norm tight frames in finitedimensional spaces

Nate Strawn  AlgebroGeometric Techniques and Geometric Insights for Finite Frames

Kasso A. Okoudjou  Preconditioning techniques in frame theory and probabilistic frames

Alexander Dunkel, Alexander M. Powell, Anneliese H. Spaeth and Özgur Yılmaz  Quantization, finite frames, and error diffusion

Radu Balan  Frames and Phaseless Reconstruction

Guangliang Chen and Deanna Needell  Compressed sensing and dictionary learning


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Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics.
This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX.
Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents stateoftheart results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the nonexpert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.
Graduate students and research mathematicians interested in frame theory and its applications.

Articles

Peter G. Casazza and Richard G. Lynch  A Brief Introduction to Hilbert Space Frame Theory and its Applications

Dustin G. Mixon  Unit norm tight frames in finitedimensional spaces

Nate Strawn  AlgebroGeometric Techniques and Geometric Insights for Finite Frames

Kasso A. Okoudjou  Preconditioning techniques in frame theory and probabilistic frames

Alexander Dunkel, Alexander M. Powell, Anneliese H. Spaeth and Özgur Yılmaz  Quantization, finite frames, and error diffusion

Radu Balan  Frames and Phaseless Reconstruction

Guangliang Chen and Deanna Needell  Compressed sensing and dictionary learning