Distributions

Generalized Functions with Applications in Sobolev Spaces
1. Auflage 2012
ISBN: 978-3-11-026927-7
Verlag: De Gruyter

Buch, Englisch, 834 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 1454 g

Reihe: De Gruyter Textbook

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 their approximate solutions on computer in particular. Almost all topics which will be essential for the study of Sobolev spaces and their applications in the elliptic boundary value problems and their finite element approximations are presented. Also many additional topics of interests for specific applied disciplines and engineering, for example, elementary solutions, derivatives of discontinuous functions of several variables, delta-convergent sequences of functions, Fourier series of distributions, convolution system of equations etc. have been included along with many interesting examples.

Zielgruppe

Graduate Students and Young Researchers in Mathematics, Physical Sciences and Engineering; Academic Libraries

Autoren/Hrsg.

Bhattacharyya, Pulin Kumar

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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 D'( O)
Chapter 5. Local properties, restrictions, unification principle, space e'(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 S' (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 S'Rn)
8.8 Laplace transform of distributions on R
8.9 Applications
8.10 Sobolev spaces on O ? Rn revisited
8.11 Compactness results in Sobolev spaces
8.12 Sobolev’s imbedding results
8.13 Sobolev spaces Hs.( G), Ws;p( G) on a manifold boundary G
8.14 Trace results in Sobolev spaces on O ?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

Über Autor(innen)

Bhattacharyya, Pulin Kumar
Pulin Kumar Bhattacharyya, Indian Institute of Technology Delhi, New Delhi, India.