Function spaces and wavelets on domains 1st Edition by Hans Triebel ISBN 3037191953 9783037191958 by Triebel H. 9783037190197, 3037190191 instant download after payment.

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ISBN 10: 3037191953 
ISBN 13: 9783037191958
Author: Hans Triebel

Function spaces and wavelets on domains 1st Table of contents:

Part I: Foundations of Function Spaces

• Chapter 1: Review of Classical Function Spaces
  • Lp spaces and Sobolev spaces on Rn.
  • Besov spaces and Triebel-Lizorkin spaces on Rn (definitions and basic properties).
  • Hardy spaces, BMO.
• Chapter 2: Function Spaces on Domains: Basic Definitions
  • Domains with smooth boundaries (Lipschitz, Ck, etc.).
  • Restriction and Extension Operators.
  • Trace Spaces and their properties.
  • Function spaces on rough domains (e.g., fractal domains, domains with corners).
• Chapter 3: Embedding Theorems and Duality
  • Sobolev embeddings on domains.
  • Duality relations for function spaces on domains.
  • Compact embeddings.

Part II: Wavelet Bases and Constructions

• Chapter 4: Basics of Wavelet Theory
  • Multiresolution Analysis (MRA) on Rn.
  • Construction of orthonormal and biorthogonal wavelet bases on Rn.
  • Properties of wavelets (regularity, vanishing moments, localization).
• Chapter 5: Wavelets on Bounded Domains: General Strategies
  • Boundary-adapted wavelets (e.g., using reflections, extensions).
  • Wavelets on intervals and their tensor products.
  • Localized boundary corrections.
  • Domain decomposition methods.
• Chapter 6: Specific Constructions of Wavelets on Domains
  • Adapted wavelet bases (e.g., via lifting schemes).
  • Wavelets on Riemannian manifolds or surfaces.
  • Construction of wavelet bases for specific boundary conditions (e.g., Dirichlet, Neumann).
  • Finite element-based wavelets.

Part III: Characterizations and Applications

• Chapter 7: Wavelet Characterizations of Function Spaces on Domains

  • Equivalence of Besov/Triebel-Lizorkin norms with wavelet coefficients on domains.
  • Applications to interpolation theory.
  • Characterization of trace spaces using wavelets.

• Chapter 8: Wavelet Methods for Partial Differential Equations (PDEs)

  • Wavelets in numerical solutions of PDEs on domains.
  • Adaptive wavelet methods for boundary value problems.
  • Preconditioning techniques using wavelets.

• Chapter 9: Wavelets in Signal and Image Processing on Domains

  • Image compression and denoising for images with boundaries.
  • Feature extraction on non-rectangular domains.
  • Inverse problems and regularization using wavelets on domains.

• Chapter 10: Further Advanced Topics

  • Wavelets on fractals and irregular domains.
  • Adaptive decompositions and nonlinear approximation on domains.
  • Shearlets, curvelets, and other directional multiscale systems on domains.
  • Applications to computational fluid dynamics or quantum mechanics.

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Tags: Hans Triebel, Function, wavelets