Frames and Other Bases in Abstract and Function Spaces: Novel Methods in Harmonic Analysis, Volume 1 (Applied and Numerical Harmonic Analysis) - Softcover

Softcover

ISBN 10: 3319856928 ISBN 13: 9783319856926

Publisher: Birkhäuser, 2018

Synopsis

The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. 

The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. 

Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as:

• The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling.
  
• A systematic approach to shearlets with applications to wavefront sets and function spaces.
  
• Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions.
  
• Kernel methods, wavelets, and frames on compact and non-compact manifolds.
  

About this title

From the Back Cover

The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. 

The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. 

Volume I is organized around the theme of frames and other bases inabstract and function spaces, covering topics such as:

• The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling.
  
• A systematic approach to shearlets with applications to wavefront sets and function spaces.
  
• Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions.
  
• Kernel methods, wavelets, and frames on compact and non-compact manifolds.

Edition details

• Publisher: Birkhäuser
• Publication date: 2018
• Language: English
• ISBN 10: 3319856928
• ISBN 13: 9783319856926
• Binding: Paperback
• Number of pages: 452
• Editor: Pesenson Isaac, Le Gia Quoc Thong, Mayeli Azita, Mhaskar Hrushikesh, Zhou Ding-Xuan