Theory of distributions
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differen...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Cham, Switzerland
Springer Nature
2021
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| Ausgabe: | Second edition |
| Schlagworte: | |
| Online Zugang: | Inhaltsverzeichnis zbMATH |
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Tag hinzufügen | Zusammenfassung: | This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This second edition, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course. The book intends to present the fundamentals of Schwartz’s theory of distributions and some applications. It has ten chapters that cover the definition, properties and operations of distributions and examples, tempered distributions and the Fourier transform, fundamental solutions and Sobolev spaces. Exercises are stated. The main changes in this edition are the following: (1) A long section about Lp spaces has been added in Chapter 1. (2) A section entitled Change of Variables has been added to Chapter 2. (3) A short section concerning the local structure of distributions is now included in Chapter 3. (4) Each chapter now finishes with a very short section called “Notes and References”. Here a summary of the chapter and a few references are included. (5) Some problems are provided with detailed proofs and the index has been updated. |
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| Beschreibung: | xi, 262 Seiten Illustrationen |
| ISBN: | 9783030812645 978-3-030-81264-5 |