An Introduction to Frames and Riesz Bases

This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems.  Compared with the first edition, more emphasis is put on explicit const...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Christensen, Ole (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
Edición:2nd ed. 2016.
Colección:Applied and Numerical Harmonic Analysis,
Temas:
Functional analysis.
Harmonic analysis.
Operator theory.
Signal processing.
Functional Analysis.
Abstract Harmonic Analysis.
Operator Theory.
Signal, Speech and Image Processing .
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Frames in Finite-dimensional Inner Product Spaces
  • Infinite-dimensional Vector Spaces and Sequences
  • Bases
  • Bases and their Limitations
  • Frames in Hilbert Spaces
  • Tight Frames and Dual Frame Pairs
  • Frames versus Riesz Bases
  • Selected Topics in Frame Theory
  • Frames of Translates
  • Shift-Invariant Systems in l2(R)
  • Gabor Frames in L2(R)
  • Gabor Frames and Duality
  • Selected Topics on Gabor Frames
  • Gabor Frames in ℓ2(Z),L2(0,L),CL
  • General Wavelet Frames in L2(R)
  • Dyadic Wavelet Frames for L2(R)
  • Frame Multiresolution Analysis
  • Wavelet Frames via Extension Principles
  • Selected Topics on Wavelet Frames
  • Generalized Shift-Invariant Systems in L2(Rd)
  • Frames on Locally Compact Abelian Groups
  • Perturbation of Frames
  • Approximation of the Inverse Frame Operator
  • Expansions in Banach Spaces. Appendix.

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