Author | Gohberg, Israel. author |
---|---|
Title | One-Dimensional Linear Singular Integral Equations [electronic resource] : I. Introduction / by Israel Gohberg, Naum Krupnik |
Imprint | Basel : Birkhรคuser Basel, 1992 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8647-5 |
Descript | 269 p. online resource |
1 The operator of singular integration -- 1.1 Notations, definitions and auxiliary statements -- 1.2 The boundedness of the operator S? in the space Lp(?) with ? being a simple curve -- 1.3 Nonsimple curves -- 1.4 Integral operators in weighted Lp spaces -- 1.5 Unbounded curves -- 1.6 The operator of singular integration in spaces of Hรถlder continuous functions -- 1.7 The operator S?* -- 1.8 Exercises -- Comments and references -- 2 One-sided invertible operators -- 2.1 Direct sum of subspaces -- 2.2 The direct complement -- 2.3 Linear operators. Notations and simplest classes -- 2.4 Projectors connected with the operator of singular integration -- 2.5 One-sided invertible operators -- 2.6 Singular integral operators and related operators -- 2.7 Examples of one-sided invertible singular integral operators -- 2.8 Two lemmas on the spectrum of an element in a subalgebra of a Banach algebra -- 2.9 Subalgebras of a Banach algebra generated by one element -- 2.10 Exercises -- Comments and references -- 3 Singular integral operators with continuous coefficients -- 3.1 The index of a continuous function -- 3.2 Singular integral operators with rational coefficients -- 3.3 Factorization of functions -- 3.4 The canonical factorization in a commutative Banach algebra -- 3.5 Proof of the factorization theorem -- 3.6 The local factorization principle -- 3.7 Operators with continuous coefficients -- 3.8 Approximate solutions of singular integral equations -- 3.9 Generalized factorizations of continuous functions -- 3.10 Operators with continuous coefficients (continuation) -- 3.11 Additional facts and generalizations -- 3.12 Operators with degenerating coefficients -- 3.13 A generalization of singular integral operators with continuous coefficients -- 3.14 Solution of Wiener-Hopf equations -- 3.15 Some applications -- 3.16 Exercises -- Comments and references -- 4 Fredholm operators -- 4.1 Normally solvable operators -- 4.2 The restriction of normally solvable operators -- 4.3 Perturbation of normally solvable operators -- 4.4 The normal solvability of the adjoint operator -- 4.5 Generalized invertible operators -- 4.6 Fredholm operators -- 4.7 Regularization of operators. Applications to singular integral operators -- 4.8 Index and trace -- 4.9 Functions of Fredholm operators and their index -- 4.10 The structure of the set of Fredholm operators -- 4.11 The Dependence of kerX and imX on the operator X -- 4.12 The continuity of the function kx -- 4.13 The case of a Hilbert space -- 4.14 The normal solvability of multiplication by a matrix function -- 4.15 ?ยฑ-operators -- 4.16 One-sided regularization of operators -- 4.17 Projections of invertible operators -- 4.18 Exercises -- Comments and references -- 5 Local Principles and their first applications -- 5.1 Localizing classes -- 5.2 Multipliers on $$ \mathop l\limitŝ \sim _p $$ -- 5.3 paired equations with continuous coefficients on $$ \mathop l\limitŝ \sim _p $$ -- 5.4 Operators of local type -- 5.5 Exercises -- Comments and references -- References