Distributions

Theory and Applications
2010. Auflage 2010
ISBN: 978-0-8176-4672-1
Verlag: Birkhauser Boston

Buch, Englisch, 445 Seiten, Format (B × H): 166 mm x 240 mm, Gewicht: 1820 g

Reihe: Cornerstones

This text offers a uniquely application-oriented introduction to the theory of distributions. It presents distributions as a natural method of analysis from both a mathematical and physical point of view. The discussion emphasizes applications to the general study of differential equations and in particular, linear partial differential equations. In this book the subject is motivated by many exercises, hints and solutions that guide the student along a path requiring only a minimal mathematical background. Advanced undergraduate and graduate students in mathematics, theoretical physics and engineering will find this textbook a welcome introduction to the theory of distributions, a subject often requiring a strong mathematical background.

Zielgruppe

Graduate

Autoren/Hrsg.

Duistermaat, J J

Kolk, Johan A C

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

Motivation.- Test Functions.- Distributions.- Differentiation of Distributions.- Convergence of Distributions.- Taylor Expansion in Several Variables.- Localization.- Distributions with Compact Support.- Multiplication by Functions.- Transposition: Pullback and Pushforward.- Convolution of Distributions.- Fundamental Solutions.- Fractional Integration and Differentiation.- Fourier Transform.- Distribution Kernels.- Fourier Series.- Fundamental Solutions and Fourier Transform.- Supports and Fourier Transform.- Sobolev Spaces.- Appendix: Integration.- Solutions to Selected Problems.

Über Autor(innen)

Hans Duistermaat was a geometric analyst, who unexpectedly passed away in March 2010. His research encompassed many different areas in mathematics: ordinary differential equations, classical mechanics, discrete integrable systems, Fourier integral operators and their application to partial differential equations and spectral problems, singularities of mappings, harmonic analysis on semisimple Lie groups, symplectic differential geometry, and algebraic geometry. He was (co-)author of eleven books.

Duistermaat was affiliated with the Mathematical Institute of Utrecht University since 1974 as a Professor of Pure and Applied Mathematics. During the last five years he was honored with a special professorship at Utrecht University endowed by the Royal Netherlands Academy of Arts and Sciences. He was also a member of the Academy since 1982. He had 23 PhD students.

Johan Kolk has published in the areas of harmonic analysis on semisimple Lie groups, the theory of distributions, and classical analysis. Jointly with Duistermaat, he has written four books: besides the present one, one on Lie groups, and another on multidimensional real analysis. Until his retirement in 2009, he was affiliated with the Mathematical Institute of Utrecht University. For more information, see http://www.staff.science.uu.nl/~kolk0101/