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Introduction to the Theory of Singular Integral Operators with Shift : Mathematics and Its Applications - Viktor G. Kravchenko

Introduction to the Theory of Singular Integral Operators with Shift

Mathematics and Its Applications

Hardcover

Published: 31st May 1994
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This book is devoted to the Fredholm theory of singular integral operators with shift in [actual symbol not reproducible] spaces. Fredholm criteria are derived and the indices of the Fredholm operators are computed. Simultaneously, a theory of continuous invertibility for functional operators is constructed, and its relation to the theory of dynamical systems is discussed. Also, a new systematic approach to the Fredholm theory of classical singular integral equations with Cauchy kernel is proposed. Detailed proofs are given throughout. The book contains an extensive survey of the literature on closely related topics.

Introduction
Background informationp. 1
On Noetherian operatorsp. 1
On the operator of singular integrationp. 15
On the shift function and shift operatorp. 26
On C*-algebrasp. 33
Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous casep. 37
Criterion of Noetherity for singular integral functional operators of first order with orientation-preserving shiftp. 40
The calculation of the index of a singular integral functional operator of the first order with a shift preserving the orientationp. 60
The Noetherity criterion and the index formula for a singular integral functional operator of the first order with a shift changing the orientationp. 81
References and a survey of similar or closed resultsp. 89
The Noether theory of a singular integral functional operator of finite order in the continuous casep. 101
The Noetherity criterion and the index formula for a system of singular integral equations with a Cauchy kernel and continuous coefficients on a closed contourp. 104
Theorems concerning decreasing the order of functional and singular integral operatorsp. 107
Noetherity criterion and a formula for the index for systems of singular integral equation with a Carleman shiftp. 113
An invertibility criterion for a matrix functional operator with a non-Carleman shiftp. 118
Noether theory for singular integral functional operators of superior ordersp. 148
References and a survey of similar resultsp. 154
The Noether theory of singular integral functional operators with continuous coefficients on a non-closed contourp. 161
The Noetherity criterion and the index formula for a singular integral operator with continuous coefficients on a non-closed contourp. 164
The Noetherity criterion and the index formula for singular integral functional operators with continuous coefficients on a non-closed contourp. 186
Systems of singular integral operators with shift on a non-closed contourp. 202
References and a survey of closely related resultsp. 208
The Noether theory in algebras of singular integral functional operatorsp. 211
C*-algebras of singular integral operatorsp. 214
C*-algebras of singular integral operators with a Carleman shiftp. 221
C*-algebras of singular integral operators with non-Carleman shift which has periodic pointsp. 228
Further development of a local method for studying the Noetherity of bounded linear operators of non-local type and its applications. Commentaries to the literaturep. 238
Referencesp. 265
Subject Indexp. 287
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792328643
ISBN-10: 0792328647
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 288
Published: 31st May 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.34