Functional Differential Equations : II. C*-Applications Part 1: Equations with Continuous Coefficients (Hardcover)

PART 1: Preface to Volume II Introduction to Volume II G-Pseudodifferential Operators with Continuous Coefficients Symbolic Calculus G-Pseudodifferential Operators on Rn. Pseudodifferential Difference Operators and Pseudodifferential Operators with Affine Shifts The Measures on the Sphere Ergodic under the Induced Linear Actions G-PDOs on Rn with "Linear" Shifts. Examples The Symbolic Calculus of G-PDOs on a Manifold L2-Case) The Symbolic Calculus of G-PDOs in Sobolev Spaces The Symbolic Calculus of G-PDOs on Vector Bundles. The Main Theorem G-PDOs with a Finite Group of Shifts G-PDOs on the Torus. Examples G-PDOs. Examples G-Singular Integral Operators with Continuous Coefficients The Index of a G-SIO G-Toeplitz Operators with Continuous Coefficients Boundary Value Problems with Strong Non-Localness The Convolution Type Operators Notes and Remarks Appendices The Index Calculation in C*(A,Tg) Quasicross-Products and C*-Algebras Associated with Quasirepresentations of Groups Notes and Remarks Bibliography Index List of Notation PART 2: Preface Preface to Volume II G-Pseudodifferential Operators with Piecewise Continuous Coefficients Symbolic Calculus of G-PDOs with Piecewise Continuous Coefficients G-PDOs with Piecewise Continuous Coefficients having Singularities on a Singled Out Set Algebras Generated by Singular Integral Operators with Piecewise Continuous Coefficients and Piecewise Smooth Mappings of a Curve Algebras Generated by Teoplitz Operators with Piecewise Continuous Coefficients and Smooth Mappings of a Curve Algebras Generate by Toeplitz Operators with Piecewise Continuous Coefficients and Piecewise Smooth Mappings of a Curve The Index Calculation for G-SIOs and G-Toeplitz Operators with Piecewise Continuous Coefficients. Kveselava-Vekua Type Theorems G-Boundary Value Problems C*-Algebras Arising from the Wiener-Hopf Operators Miscellaneous Results. PDOs with the Transmission Property The Boutet de Monvel Operators of the Class B0 The Spectrum of the C*-Algebra of the Principal Symbols of Elements of B0 G-Boutet de Monvel Operators (G-BMOs) G-Boundary Value Problem Operators (G-BVPOs) I G-BVPOs II Example G-BVPOs III Non-Local Agranovich-Dynin Type Theorem Transmission Problems G-BVPOs in Sobolev Spaces The Localization Theorem. Reduction of G-BVPOs to G-BMOs Notes and Remarks Appendix C C*-Algebras Associated with Automorphisms Acting on a Singled Out Ideal Notes and Remarks Bibliography Index List of Notation