Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift / by Georgii S. Litvinchuk
(Mathematics and Its Applications ; 523)
| データ種別 | 電子ブック |
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| 出版情報 | Dordrecht : Springer Netherlands : Imprint: Springer , 2000 |
| 本文言語 | 英語 |
| 大きさ | XVI, 378 p : online resource |
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| 内容注記 | 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 36 Approximate 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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| 一般注記 | The first formulations of linear boundary value problems for analytic functions were due to Riemann (1857). In particular, such problems exhibit as boundary conditions relations among values of the unknown analytic functions which have to be evaluated at different points of the boundary. Singular integral equations with a shift are connected with such boundary value problems in a natural way. Subsequent to Riemann's work, D. Hilbert (1905), C. Haseman (1907) and T. Carleman (1932) also considered problems of this type. About 50 years ago, Soviet mathematicians began a systematic study of these topics. The first works were carried out in Tbilisi by D. Kveselava (1946-1948). Afterwards, this theory developed further in Tbilisi as well as in other Soviet scientific centers (Rostov on Don, Ka zan, Minsk, Odessa, Kishinev, Dushanbe, Novosibirsk, Baku and others). Beginning in the 1960s, some works on this subject appeared systematically in other countries, e. g. , China, Poland, Germany, Vietnam and Korea. In the last decade the geography of investigations on singular integral operators with shift expanded significantly to include such countries as the USA, Portugal and Mexico. It is no longer easy to enumerate the names of the all mathematicians who made contributions to this theory. Beginning in 1957, the author also took part in these developments. Up to the present, more than 600 publications on these topics have appeared |
| 著者標目 | *Litvinchuk, Georgii S. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Difference equations LCSH:Functional equations LCSH:Functions of complex variables LCSH:Integral equations LCSH:Operator theory LCSH:Potential theory (Mathematics) FREE:Mathematics FREE:Integral Equations FREE:Functions of a Complex Variable FREE:Operator Theory FREE:Potential Theory FREE:Difference and Functional Equations |
| 分 類 | DC23:515.45 |
| 巻冊次 | ISBN:9789401143639 
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| ISBN | 9789401143639 |
| URL | http://dx.doi.org/10.1007/978-94-011-4363-9 |
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