Author(s): Georgi E. Shilov
Series: Mathematics and its Applications, Vol. 7
Publisher: Gordon & Breach Science Publishers Ltd
Year: 1968
Language: English
Pages: xii+345
Cover
S Title
List of Published Mathematics and Its Applications
Generalized Functions and Partial Differential Equations
Copyright
© 1968 BY GORDON AND BREACH
ISBN-10: 0677206607
ISBN-13: 9780677206608
Library of Congress Catalog Card Number 67-28235
Contents
Preface
Part 1 GENERALIZED FUNCTIONS
Chapter 1 Elementary Theory of Generalized Functions
1.1. Problem of Extending the Collection of Ordinary Functions
1.2. Test Functions of One Variable
Problems
1.3. Generalized Functions of One Variable
Problems
1.4. Operations on Generalized Functions of One Variable
Problems
1.5. Ordinary Differential Equations
Problems
1.6. Test Functions and Generalized Functions of Several Variables
Problems
1.7. Operations on Generalized Functions of Several variables
Problems
Chapter 2 Special Topics in Generalized Function Theory
2.1. Local Properties and the Support of a Generalized Function
Problems
2.2. Convergence in the Space of Generalized Functions
Problems
2.3. The Structure of Generalized Functions
Problems
2.4. Special Generalized Functions
Problems
2.5. Convolutions of Generalized Functions
Problems
2.6. Order of Singularity
Problem
2.7. Fourier Transforms of Generalized Functions
Problems
2.8. Fourier Transforms of Generalized Functions (Continuation)
Problems
Part 2 PROBLEMS IN THE GENERAL THEORY OF PARTIAL DIFFERENTIAL EQUATIONS
Chapter 3 Fundamental Functions of Differential Operators and Local Properties of Solutions
3.1. A Poisson Type Formula
Problems
3.2. Existence of a Fundamental Function
Problems
3.3. An Equation with Might-Hand Side
Problems
3.4. A Condition for Hypoellipticity Based on the Zeros of P(s) (Necessity)
Problems
3.5. A Condition for Hypoellipticity Based on the Zeros of P(s) (Sufficiency)
Problems
3.6. Conditions for Hypoellipticity Based on the Behavior of P(s) in the Real Domain
Problems
3.7. Radon's Method
Problems
Chapter 4 Equations in a Half-Space
4.1. Well-Posed Boundary Value Problems
Problem
4.2. Subsidiary Information
4.3. Ordinary Differential Equations and Systems
4.4. Partial Differential Equations
4.5. Fundamental Solutions of Regular Boundary Value Problems
Problems
4.6. Formulas for Fundamental Solutions of Regular Equations (n = 1)
Problems
4.7. Fundamental Solutions of Regular Equations (n > 1)
4.8. An Equation with Right-Hand Side
4.9. Mixed problems
Bibliographical Comments
Index
Back Cover
