Generalized functions and partial differential equations

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


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