# Generalized Functions And Partial Differential Equations

## Friedman, Avner

Valutazione media 4
( su 2 valutazioni fornite da Goodreads ) Vedi tutte le copie di questo ISBN:

This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research.
Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

1 Linear Topological Spaces 1. Topological spaces and metric spaces 2. Linear topological spaces 3. Countably normed spaces 4. Continuous linear functionals 5. Weak and strong topologies 6. Perfect spaces 7. Linear operators 8. Inductive limits and unions of topological spaces Problems 2 Spaces of Generalized Functions 1. Fundamental spaces and generalized functions 2. The spaces K{Mp} 3. The spaces Z{Mp} 4. Multiplication and the derivatives of generalized functions 5. Structure of generalized functions on K{Mp} Problems 3 Theory of Distributions 1. Spaces of functions 2. Partition of unity 3. Definition and some properties of distributions 4. Derivatives of distributions 5.-6. Structure of distributions 7. Distributions having support on compact sets or on subspaces 8. Tensor product of distributions 9. Product of distributions by functions Applications to differential equations 10. Convolutions of distributions 11. Convolutions of distributions with smooth functions 12. The spaces Kr{Mp}, {DLr} and the structure of their generalized functions 13. Convolution equations 14. The spaces (S) and (S') 15. Fourier transforms of distributions Problems 4 Convolutions and Fourier Transforms of Generalized Functions 1. Fourier transforms of fundamental functions 2. Fourier transforms of generalized functions 3. Convolutions of generalized functions 4. The convolution theorems Problems 5 W Spaces 1. Theorems on complex analytic functions 2. Definition of W spaces 3. Operators in W spaces 4. Fourier transforms of W spaces 5. Nontriviality and richness of W spaces Problems 6 Fourier Transforms of Entire Functions 1. Entire functions of order equal or less than p and of fast decrease 2. Entire functions of order equal or less than 1 3. Entire functions of order equal or less than 1 and of slow increase 4. Entire functions of order equal or less than p and of slow increase 5. Entire functions of order equal or less than p and of mildly fast increase 6. Entire functions of order equal or less than p and of fast increase 7. Proof of Lemma 2 Problems 7 The Cauchy Problem for Systems of Partial Differential Equations 1. Systems of partial differential equations and the Cauchy problem 2. Auxiliary theorems on functions of matrices 3. Uniqueness of solutions of the Cauchy problem 4. Existence of generalized solutions 5. Lemmas on convolutions 6. Existence theorems for parabolic systems 7. An existence theorem for hyperbolic systems 8. Existence theorems for correctly posed systems 9. Existence theorems for mildly incorrectly posed systems 10. An existence theorem for incorrectly posed systems 11. Nonhomogeneous systems with time-dependent coefficients 12. Systems of convolution equations 13. Difference-differential equations 14. Inverse theorems 15. Proof of the Seidenberg-Tarski theorem Problems 8 The Cauchy Problem in Several Time Variables 1. Uniqueness and existence of generalized solutions 2. Sobolev's lemma 3. Proof of Theorem 4. Existence of classical solutions 5. The Goursat problem Problems 9 S Spaces 1. Definition of S spaces 2. Operators in S spaces 3. Fourier transforms of S spaces 4. Nontriviality and richness of S spaces Problems 10 Further Applications to Partial Differential Equations 1. A Phragm�n-Lindel�f type theorem 2. A Liouville type theorem 3. Fundamental solutions of equations with constant coefficients 4. Special distributions and Radon's problem 5. Fundamental solutions for hyperbolic equations Problems 11 Differentiability of Solutions of Partial Differential Equations 1. Hypoelliptic equations and their fundamental solutions 2.-3. Conditions for hypoellipticity 4. Examples of hypoelliptic equations 5. Nonhomogeneous equations Problems Bibliographical Remarks Bibliography Index for Spaces Index

Product Description:

This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. It covers Cauchy and Goursat problems, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. 1963 edition

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

## 1.GENERALIZED FUNCTIONS AND PARTIA

ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Quantit�: 1
Da
Best Bates
(Bensalem, PA, U.S.A.)

Descrizione libro Condizione: New. . Codice articolo 52YZZZ00D77G_ns

Compra nuovo
EUR 13,58
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 2.GENERALIZED FUNCTIONS AND PARTIA

ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Quantit�: 1
Da
PublisherOverstocks
(Taunton, MA, U.S.A.)

Descrizione libro Condizione: New. . Codice articolo 533ZZZ00CII8_ns

Compra nuovo
EUR 13,58
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 3.GENERALIZED FUNCTIONS AND PARTIA

ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Quantit�: 1
Da
Bookhouse

Descrizione libro Condizione: New. . Codice articolo 532ZZZ00CINF_ns

Compra nuovo
EUR 13,58
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 4.Generalized Functions and Partial Differential Equations (Dover Books on Mathematics)

Editore: Dover Publications
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Quantit�: 10
Da
Lakeside Books
(Benton Harbor, MI, U.S.A.)

Descrizione libro Dover Publications. Condizione: New. Brand New Direct from the Publisher! Not overstocks or marked up remainders! Ships in a sturdy cardboard container with tracking!|VCF. Codice articolo OTF-S-9780486446103

Compra nuovo
EUR 10,46
Convertire valuta
Spese di spedizione: EUR 3,28
In U.S.A.
Destinazione, tempi e costi

## 5.Generalized Functions and Partial Differential Equations (Paperback or Softback)

Editore: Dover Publications 12/10/2005 (2005)
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Paperback or Softback Quantit�: 5
Da
BargainBookStores
(Grand Rapids, MI, U.S.A.)

Descrizione libro Dover Publications 12/10/2005, 2005. Paperback or Softback. Condizione: New. Generalized Functions and Partial Differential Equations. Book. Codice articolo BBS-9780486446103

Compra nuovo
EUR 14,25
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 6.Generalized Functions and Partial Differential Equations (Dover Books on Mathematics)

Editore: Dover Publications
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Soft cover Quantit�: 1
Da
Newsboy Books
(Ontario, CA, U.S.A.)

Descrizione libro Dover Publications. Soft cover. Condizione: New. 0486446107 New. Retail 19.95. Codice articolo 0486446107NE

Compra nuovo
EUR 11,84
Convertire valuta
Spese di spedizione: EUR 3,12
In U.S.A.
Destinazione, tempi e costi

## 7.Generalized Functions and Partial Differential Equations (Paperback)

Editore: Dover Publications Inc., United States (2006)
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Paperback Quantit�: 1
Da
The Book Depository
(London, Regno Unito)

Descrizione libro Dover Publications Inc., United States, 2006. Paperback. Condizione: New. Language: English. Brand new Book. This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography. Codice articolo AAZ9780486446103

Compra nuovo
EUR 16,28
Convertire valuta
Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

## 8.Generalized Functions and Partial Differential Equations

Editore: Dover (2006)
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Paper Back Quantit�: 1
Da
Technical Book Store
(Malabar, FL, U.S.A.)

Descrizione libro Dover, 2006. Paper Back. Condizione: New. NEW BOOK. Codice articolo 033465

Compra nuovo
EUR 14,35
Convertire valuta
Spese di spedizione: EUR 4,73
In U.S.A.
Destinazione, tempi e costi

## 9.Generalized Functions and Partial Differential Equations (Dover Books on Mathematics)

Editore: Dover Publications (2005)
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Brossura Quantit�: 1
Da
GlassFrogBooks
(Hawthorne, CA, U.S.A.)

Descrizione libro Dover Publications, 2005. Condizione: New. A+ Customer service! Satisfaction Guaranteed! Book is in NEW condition. Codice articolo 0486446107-2-1

Compra nuovo
EUR 19,36
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 10.Generalized Functions and Partial Differential Equations

Editore: DOVER PUBN INC (1900)
ISBN 10: 0486446107 ISBN 13: 9780486446103
Nuovo Softcover Quantit�: > 20
Da
Russell Books