Overview

This text is devoted to the solvability theory of characteristic singular integral equations and corresponding boundary value problems for analytic functions with a Carleman and non-Carleman shift. The defect numbers are computed and the bases for the defect subspaces are constructed. Applications to mechanics, physics, and geometry of surfaces are discussed. The second part of the book also contains an extensive survey of the literature on closely related topics. While the first part of the book is also accessible to engineers and undergraduate students in mathematics, the second part is aimed at specialists in the field.

Full Product Details

Author:   Georgii S. Litvinchuk
Publisher:   Springer
Imprint:   Springer
Edition:   2000 ed.
Volume:   523
Dimensions:   Width: 17.00cm , Height: 2.30cm , Length: 24.40cm
Weight:   1.640kg
ISBN:  

9780792365495

ISBN 10:   0792365496
Pages:   378
Publication Date:   30 September 2000
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Preliminaries.- 1 On Noether operators.- 2 Shift function.- 3 Operator of singular integration, shift operator, operator of complex conjugation and certain combinations of them.- 4 Singular integral operators with Cauchy kernel.- 5 Riemann boundary value problems.- 6 The Noether theory for singular integral operators with a Carleman shift and complex conjugation.- 2 Binomial boundary value problems with shift for a piecewise analytic function and for a pair of functions analytic in the same domain.- 7 The Hasemann boundary value problem.- 8 Boundary value problems which can be reduced to a Hasemann boundary value problem.- 9 References and a survey of closely related results.- 3 Carleman boundary value problems and boundary value problems of Carleman type.- 10 Carleman boundary value problems.- 11 Boundary value problems of Carleman type.- 12 Geometric interpretation of the conformai gluing method.- 13 References and a survey of closely related results.- 4 Solvability theory of the generalized Riemann boundary value problem.- 14 Solvability theory of the generalized Riemann boundary value problem in the stable and degenerated cases.- 15 References and a survey of similar or related results.- Solvability theory of singular integral equations with a Carleman shift and complex conjugated boundary values in the degenerated and stable cases.- 16 Characteristic singular integral equation with a Carleman shift in the degenerated cases.- 17 Characteristic singular integral equation with a Carleman shift and complex conjugation in the degenerated cases.- 18 Solvability theory of a singular integral equation with a Carleman shift and complex conjugation in the stable cases.- 19 References and a survey of similar or related results.- 6 Solvability theory of general characteristic singular integral equations with a Carleman fractional linear shift on the unit circle.- 20 Characteristic singular integral equation with a direct Carleman fractional linear shift.- 21 Characteristic singular integral equation with an inverse Carleman fractional linear shift.- 22 References and survey of closed and related results.- 7 Generalized Hilbert and Carleman boundary value problems for functions analytic in a simply connected domain.- 23 Noether theory of a generalized Hilbert boundary value problem.- 24 Solvability theory of generalized Hilbert boundary value problems.- 25 Noetherity theory of a generalized Carleman boundary value problem.- 26 Solvability theory of a generalized Carleman boundary value problem.- 27 References and a survey of similar or related results.- 8 Boundary value problems with a Carleman shift and complex conjugation for functions analytic in a multiply connected domain.- 28 Integral representations of functions analytic in a multiply connected domain.- 29 The Noether theory of a generalized Carleman boundary value problem with a direct shift ? = ?+(t) in a multiply connected domain.- 30 The solvability theory of a binomial boundary value problem of Carleman type in a multiply connected domain.- 31 The solvability theory of a Carleman boundary value problem in a multiply connected domain.- 32 The Noether theory of a generalized Carleman boundary value problem with an inverse shift ? = ?_ for a multiply connected domain.- 33 References and a survey of similar or related results.- 9 On solvability theory for singular integral equations with a non-Carleman shift.- 34 Auxiliary Lemmas.- 35 Estimate for the dimension of the kernel of a singular integral operator with a non-Carleman shift having a finite number of fixed points.- 36Approximate solution of a non-homogeneous singular integral equation with a nonCarleman shift.- 37 Singular integral equations with non-Carleman shift as a natural model for problems of synthesis of signals for linear systems with non-stationary parameters.- References.

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