Distributions, Volume 3 1st Edition

Distributions, Volume 3 1st Edition – Ebook Instant Download/Delivery ISBN(s): 9781786305251,9781394165346,9781394165353,1786305259,139416534X,1394165358

Product details:

• ISBN 10:1394165358
• ISBN 13:9781394165353
• Author: Jacques Simon

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 Fréchet 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.

Table contents:

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

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