Distributions and convolution equations /
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| Author / Creator: | Gindikin, S. G. (Semen Grigorʹevich) |
|---|---|
| Imprint: | Philadelphia : Gordon and Breach Science Publishers, c1992. |
| Description: | xi, 465 p. : ill. ; 24 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1102200 |
Table of Contents:
- Ch. 1. Convolution Equations in Spaces of Strongly Decreasing and Slowly Increasing Functions and Distributions. 1. Spaces of Testfunctions and Distributions. 2. The Scale of Hilbert Spaces Associated with [actual symbols not reproducible] (Sobolev Spaces). 3. Convolution in Spaces of Tempered Distributions. 4. Convolution Equations in Spaces of Smooth Functions and Tempered Distributions on [actual symbols not reproducible]. 5. The Spaces [actual symbols not reproducible] and the Related Scales. 6. Spaces of Functions Having Different Degrees of Smoothness with Respect to Different Variables. Kernel Theorems. Appendix to Chapter 1. Scales of Topological Linear Spaces and their Inductive and Projective Limits
- Ch. 2. Homogeneous Cauchy Problem for Convolution Equations in Spaces of Strongly Decreasing and Slowly Increasing Functions and Distributions. 1. Spaces of Functions and Distributions with Support in the Half-space [actual symbols not reproducible]. 2. Scales of Factor Spaces. 3. Scales of Spaces of Functions Defined in [actual symbols not reproducible]. 4. Convolution Operators and Convolution Equations in Spaces of Functions and Distributions with Support in [actual symbols not reproducible] and in a Finite Strip. 5. Convolutors and Convolution Equations in Spaces of Functions Satisfying Exponential Estimates
- Ch. 3. Convolution Equations in Spaces of Exponentially Decreasing and Increasing Functions and Distributions. 1. Scales of Spaces of Exponentially Decreasing Functions. Exponentially Increasing (Decreasing) Distributions. Convolution Equations. 2. The Homogeneous Cauchy Problem in Spaces of Exponentially Decreasing and Increasing Functions and Distributions in [actual symbols not reproducible]. 3. The Homogeneous Cauchy Problem in a Finite Strip for Spaces of Exponentially Decreasing and Increasing Functions and Distributions. 4. Exponentially Correct Differential Operators
- Ch. 4. Nonhomogeneous Cauchy Problem for Convolution Equations. 1. Scales of Spaces of Distributions Having a Higher Degree of Smoothness for t > 0 and Convolution Equations in these Scales (The One-dimensional Case). 2. Scales of Spaces of Distributions Having a Higher Degree of Smoothness for t > 0 and Convolution Equations in these Scales (The Multidimensional Case)
- Ch. 5. Cauchy Problem for Differential and Pseudodifferential Equations with Variable Coefficients. 1. Homogeneous Cauchy Problem for PDO in Scales of Spaces Related to [actual symbols not reproducible]. 2. Homogeneous Cauchy Problem for PDO in Scales of Spaces Related to [actual symbols not reproducible]. 3. Pseudodifferential Equations in [actual symbols not reproducible] (the Case of the Spaces [actual symbols not reproducible] and the Related Scales). 4. Exponentially Correct Differential Operators with Variable Coefficients
- Ch. 6. Wiener-Hopf Convolutors and Boundary Value Problems for Convolution Equations. 1. Wiener-Hopf Convolutors. 2. Factorization of Wiener-Hopf Convolutors. 3. The Wiener-Hopf Equation on a Half-line. 4. The Wiener-Hopf Equation in a Half-space.