Description
Book SynopsisThe six-volume collection,
Generalized Functions, written by I.M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.
Table of Contents
- Volume 1: Definition and simplest properties of generalized functions
- Fourier transforms of generalized functions
- Particular types of generalized functions
- Summary of fundamental definitions and equations of volume I
- Table of Fourier transforms
- Proof of the completeness of the generalized-function space
- Generalized functions of complex variables
- Notes and references to the literature
- Bibliography
- Index
- Index of particular generalized functions
- Volume 2: Linear topological spaces
- Fundamental and generalized functions
- Fourier transformations of fundamental and generalized functions
- Spaces of type $S$
- Generalization of spaces of type $S$
- Notes and references
- Bibliography
- Index
- Volume 3: Spaces of type $W$
- Uniqueness classes for the Cauchy problem
- Correctness classes for the Cauchy problem
- Generalized eigenfunction expansions
- Notes and references
- Bibliography
- Index
- Volume 4: The kernel theorem
- Nuclear spaces
- Rigged Hilbert space
- Positive and positive-definite generalized functions
- Generalized random processes
- Measures in linear topological spaces
- Notes and references to the literature
- Bibliography
- Subject index
- Volume 5: Radon transform of test functions and generalized functions on a real affine space
- Integral transforms in the complex domain
- Representations of the group of complex unimodular matrices in two dimensions
- Harmonic analysis on the group of complex unimodular matrices in two dimensions
- Integral geometry in a space of constant curvature
- Harmonic analysis on spaces homogeneous with respect to the Lorentz group
- Representations of the group of real unimodular matrices in two dimensions
- Notes and references to the literature
- Bibliography
- Index
- Index of Radon transforms of particular functions
- Volume 6: Homogeneous spaces with a discrete stability group
- Representations of the group of unimodular matrices of order 2 with elements from a locally compact topological field
- Representations of adele groups
- Guide to the literature
- Bibliography
- Index of names
- Subject index
