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Distributions, partial differential equations, and harmonic analysis / Dorina Mitrea.

By: Material type: TextTextSeries: UniversitextPublication details: New York : Springer-Verlag, 2013.Description: xxi, 460 p. ; 24 cmISBN:
  • 9781461482079 (pbk. : alk. paper)
Subject(s): DDC classification:
  • 515.353 23 M684
Contents:
Introduction.- 1. Weak Derivatives.- 2. The Space D0() of Distributions.- 3. The schwartz space and the Fourier Transform.- 4. The Space of Tempered Distributions.- 5. The Concept of a Fundamental Solution.- 7. The Laplace and Related Operator.- 8. The Heat Operator and Related Versions.- 9. The Wave Operator.- 10. The Lame and Stokes Operator.- 11. More on Fundamental Solutions for Systems.- 12. Solutions to Selected Exercises-- 13. Appendix.- Bibliography-- Indexes.
Summary: "The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity."--Page [4] of cover.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.353 M684 (Browse shelf(Opens below)) Available 135756
Total holds: 0

Includes bibliographical references (pages 449-453) and index.

Introduction.-
1. Weak Derivatives.-
2. The Space D0() of Distributions.-
3. The schwartz space and the Fourier Transform.-
4. The Space of Tempered Distributions.-
5. The Concept of a Fundamental Solution.-
7. The Laplace and Related Operator.-
8. The Heat Operator and Related Versions.-
9. The Wave Operator.-
10. The Lame and Stokes Operator.-
11. More on Fundamental Solutions for Systems.-
12. Solutions to Selected Exercises--
13. Appendix.-
Bibliography--
Indexes.

"The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity."--Page [4] of cover.

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