Distributions : : Generalized Functions with Applications in Sobolev Spaces /

Distributions : : Generalized Functions with Applications in Sobolev Spaces / / Pulin Kumar Bhattacharyya.

This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc., who were interested in studying the problems of mathematical physics in general and t...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
VerfasserIn:
Bhattacharyya, Pulin Kumar,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2012]
©2012
Year of Publication:2012
Language:English
Series:De Gruyter Textbook
Online Access:
Physical Description:1 online resource (834 p.)
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Table of Contents:
  • Frontmatter
  • Preface
  • Contents
  • How to use this book in courses
  • Acknowledgment
  • Notation
  • Chapter 1. Schwartz distributions
  • Chapter 2. Differentiation of distributions and application of distributional derivatives
  • Chapter 3. Derivatives of piecewise smooth functions, Green’s formula, elementary solutions, applications to Sobolev spaces
  • Chapter 4. Additional properties of Dʹ(Ω)
  • Chapter 5. Local properties, restrictions, unification principle, space ℰʹ(ℝn) of distributions with compact support
  • Chapter 6. Convolution of distributions
  • Chapter 7. Fourier transforms of functions of L1(ℝn) and S(ℝn)
  • Chapter 8. Fourier transforms of distributions and Sobolev spaces of arbitrary order HS(ℝn)
  • 8.1 Motivation for a possible definition of the Fourier transform of a distribution
  • 8.2 Space Sʹ (Rn) of tempered distributions
  • 8.3 Fourier transform of tempered distributions
  • 8.4 Fourier transform of distributions with compact support
  • 8.5 Fourier transform of convolution of distributions
  • 8.6 Derivatives of Fourier transforms and Fourier transforms of derivatives of tempered distributions
  • 8.7 Fourier transform methods for differential equations and elementary solutions in Sʹ(ℝn)
  • 8.8 Laplace transform of distributions on ℝ
  • 8.9 Applications
  • 8.10 Sobolev spaces on Ω ≠ Rn revisited
  • 8.11 Compactness results in Sobolev spaces
  • 8.12 Sobolev’s imbedding results
  • 8.13 Sobolev spaces Hs.(Γ), Ws;p(Γ) on a manifold boundary Γ
  • 8.14 Trace results in Sobolev spaces on Ω⊊ℝn
  • Chapter 9. Vector-valued distributions
  • Appendix A. Functional analysis (basic results)
  • Appendix B. Lp-spaces
  • Appendix C. Open cover and partition of unity
  • Appendix D. Boundary geometry
  • Bibliography
  • Index

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