Description: 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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