Distributions / Jacques Simon.

Format:

Book

Author/Creator:

Simon, Jacques, author.

Series:

Mathematics and statistics series (ISTE)

Analysis for PDEs set ; v. 3.

Mathematics and statistics series. Analysis for PDEs set ; volume 3

Language:

English

Subjects (All):

Theory of distributions (Functional analysis).

Physical Description:

1 online resource (408 pages)

Edition:

1

Place of Publication:

Wiley 2022

Summary:

This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encompasses the Banach and Fřchet spaces and the same "weak" spaces. Alongside the usual operations - derivation, product, variable change, variable separation, restriction, extension and regularization - Distributions presents a new operation: weighting. This operation produces properties similar to those of convolution for distributions defined in any open space. Emphasis is placed on the extraction of convergent sub-sequences, the existence and study of primitives and the representation by gradient or by derivatives of continuous functions. Constructive methods are used to make these tools accessible to students and engineers.

Contents:

Half-Title Page Introduction Notations Chapter 1. Semi-Normed Spaces and Function Spaces Chapter 2. Space of Test Functions Chapter 3. Space of Distributions Chapter 4. Extraction of Convergent Subsequences Chapter 5. Operations on Distributions Chapter 6. Restriction, Gluing and Support Chapter 7. Weighting Chapter 8. Regularization and Applications Chapter 9. Potentials and Singular Functions Chapter 10. Line Integral of a Continuous Field Chapter 11. Primitives of Functions Chapter 12. Properties of Primitives of Distributions Chapter 13. Existence of Primitives Chapter 14. Distributions of Distributions Chapter 15. Separation of Variables Chapter 16. Banach Space Valued Distributions Other titles from iSTE in Mathematics and Statistics EULA

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Simon, Jacques Distributions

ISBN:

9781394165360

1394165366

9781394165346

139416534X

OCLC:

1340403704