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Integral Equations with Difference Kernels on Finite Intervals

Part of the Operator Theory: Advances and Applications Book Series (volume 84)

DOI: 10.1007/978-3-319-16489-2

ISBN: 978-3-319-16488-5

Publisher: Springer International Publishing - Springer Journals

Apr 7, 2015

1 - 10 of 11 Chapters

LitStream

Chapter 1Invertible Operator with a Difference Kernel

Sakhnovich, Lev A.

Pages: 1 –30

[In this chapter, we deal with the problem of inversion of the operators S acting in the space L2(0, ω) and having the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 2Equations of the First Kind with a Difference Kernel

Sakhnovich, Lev A.

Pages: 31 –52

[In this chapter we consider again the equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Chapter 3Examples and Applications

Sakhnovich, Lev A.

Pages: 53 –86

[In this chapter, we consider a number of concrete examples and find the corresponding functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 4Eigensubspaces and Fourier Transform

Sakhnovich, Lev A.

Pages: 87 –99

[Consider a bounded operator S (in the space LP) of the form 4.0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 5Integral Operators with W-Difference Kernels

Sakhnovich, Lev A.

Pages: 101 –112

[In Section 5.1 we consider a set of the operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
LitStream

Chapter 6Problems of Communication Theory

Sakhnovich, Lev A.

Pages: 113 –123

[A stochastic process X(t) is called stationary in the wide sense if the mathematical expectation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 7Lévy Processes: Convolution-type Form of the Infinitesimal Generator

Sakhnovich, Lev A.

Pages: 125 –134

[Let us introduce the notion of Lévy processes.]
LitStream

Chapter 8On the Probability that the Lévy Process (Class II) Remains within the Given Domain

Sakhnovich, Lev A.

Pages: 135 –166

[Recall that by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$p(t,\Delta)$$...
LitStream

Chapter 9Triangular Factorization and Cauchy Type Lévy Processes

Sakhnovich, Lev A.

Pages: 167 –185

[Let us introduce the main notions of the triangular factorization (see [82, 88, 92, 96]). First, we define the orthogonal projectors Pξ in the Hilbert space L2(a, b) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...
LitStream

Chapter 10Lévy Processes with Summable Lévy Measures, Long Time Behavior

Sakhnovich, Lev A.

Pages: 187 –204

[In Chapter 7 we proved that the infinitesimal generators L for Lévy processes Xt can be represented in a convolution-type form. In the case of a non-summable Lévy measure we constructed a quasi-potential operator B and investigated the long time behavior of tt (Chapters 8 and 9).]

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