Equations with Involutive Operators

1 On Fredholmness of Singular Type Operators.- 1 Fredholm operators.- 2 Singular integral operators with piecewise continuous coefficients in the space Lp(?).- 3 On Fredholmness of convolution type operators.- 4 Bibliographic notes to Chapter 1.- 2 On Fredholmness of Other Singular-type Operators.- 5 On operators with homogeneous kernels; the one-dimensional case.- 6 Operators with homogeneous kernels; the multi-dimensional case.- 7 Convolution-type operators with discontinuous symbols.- 8 Bibliographic notes to Chapter 2.- 3 Functional and Singular Integral Equations with Carleman Shifts in the Case of Continuous Coefficients.- 9 Carleman and generalized Carleman shifts1ll.- 10 A functional equation with shift.- 11 Singular integral equations with Carleman shift on a closed curve; the case of continuous coefficients.- 12 Singular integral equations with Carleman shift on an open curve; the case of continuous coefficients.- 13 Bibliographic notes to Chapter 3.- 4 Two-term Equations (A + QB)? = f with an Involutive Operator Q; an Abstract Approach and Applications.- 14 Fredholmness of an abstract equation with an involutive operator; non-matrix approach.- 15 Application to singular integral equations with complex conjugate unknowns.- 16 Applications to integral equations on the real line with reflection or inversion.- 17 Application to singular integral equations with Carleman shift on an open curve; the case of discontinuous coefficients.- 18 Singular integral equations with a fractional linear shift in the space Lp with a special weight.- 19 Fredholmness of abstract equations with a generalized involutive operator (non-matrix approach).- 20 Abstract equations with algebraic operators.- 21 Bibliographic notes to Chapter 4.- 5 Equations with Several GeneralizedInvolutive Operators. Matrix Abstract Approach and Applications.- 22 Fredholmness of abstract equations with generalized involutive operators (matrix approach).- 23 Singular integral equations with a finite group of shifts in the case of continuous coefficients.- 24 Singular integral equations with a finite group of shifts (the case of piecewise continuous coefficients).- 25 Convolution type equations with shifts and complex conjugation.- 26 Bibliographic notes to Chapter 5.- 6 Application of the Abstract Approach to Singular Equation on the Real Line with Fractional Linear Shift.- 27 Singular integral operators perturbed by integral operators with homogeneous kernels.- 28 Singular integral operators with a fractional linear Carleman shift in the weighted space Lp?(Rl).- 29 Equations including operators with homogeneous kernels, the singular integral operators and the inversion shift.- 30. Potential type operators on the real 1ine with a fractional linear Carleman shift.- 31 Generalized Carleman fractional linear shifts on the real line . ..- 32 Singular integral equations with a generalized Carleman fractional linear shift.- 33. Bibliographic Notes to Chapter 6.- 7 Application to Hankel Type and Multidimensional Integral Equations.- 34 Convolution integral equations of Hankel type.- 35 Some multidimensional singular type equations with shifts.- 36 Bibliographic Notes to Chapter 7.- List of Symbols.