## ＜電子ブック＞One-Dimensional Linear Singular Integral Equations : I. Introduction

責任表示 by Israel Gohberg, Naum Krupnik Gohberg, Israel Krupnik, Naum SpringerLink (Online service) English (英語) Birkhäuser Basel 1992- Basel, Switzerland シリーズ Operator Theory: Advances and Applications ; 53 This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attent...ion, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form. In this book material of the monograph [2] of the authors on one-dimensional singular integral operators is widely used. This monograph appeared in 1973 in Russian and later in German translation [3]. In the final text version the authors included many addenda and changes which have in essence changed character, structure and contents of the book and have, in our opinion, made it more suitable for a wider range of readers. Only the case of singular integral operators with continuous coefficients on a closed contour is considered herein. The case of discontinuous coefficients and more general contours will be considered in the second volume. We are grateful to the editor Professor G. Heinig of the volume and to the translators Dr. B. Luderer and Dr. S. Roch, and to G. Lillack, who did the typing of the manuscript, for the work they have done on this volume.続きを見る 1 The operator of singular integration1.1 Notations, definitions and auxiliary statements1.2 The boundedness of the operator S? in the space Lp(?) with ? being a simple curve1.3 Nonsimple curves1.4 Integral operators in weighted Lp spaces1.5 Unbounded curves1.6 The operator of singular integration in spaces of Hölder continuous functions1.7 The operator S?*1.8 ExercisesComments and references2 One-sided invertible operators2.1 Direct sum of subspaces2.2 The direct complement2.3 Linear operators. Notations and simplest classes2.4 Projectors connected with the operator of singular integration2.5 One-sided invertible operators2.6 Singular integral operators and related operators2.7 Examples of one-sided invertible singular integral operators2.8 Two lemmas on the spectrum of an element in a subalgebra of a Banach algebra2.9 Subalgebras of a Banach algebra generated by one element2.10 ExercisesComments and references3 Singular integral operators with continuous coefficients3.1 The index of a continuous function3.2 Singular integral operators with rational coefficients3.3 Factorization of functions3.4 The canonical factorization in a commutative Banach algebra3.5 Proof of the factorization theorem3.6 The local factorization principle3.7 Operators with continuous coefficients3.8 Approximate solutions of singular integral equations3.9 Generalized factorizations of continuous functions3.10 Operators with continuous coefficients (continuation)3.11 Additional facts and generalizations3.12 Operators with degenerating coefficients3.13 A generalization of singular integral operators with continuous coefficients3.14 Solution of Wiener-Hopf equations3.15 Some applications3.16 ExercisesComments and references4 Fredholm operators4.1 Normally solvable operators4.2 The restriction of normally solvable operators4.3 Perturbation of normally solvable operators4.4 The normal solvability of the adjoint operator4.5 Generalized invertible operators4.6 Fredholm operators4.7 Regularization of operators. Applications to singular integral operators4.8 Index and trace4.9 Functions of Fredholm operators and their index4.10 The structure of the set of Fredholm operators4.11 The Dependence of kerX and imX on the operator X4.12 The continuity of the function kx4.13 The case of a Hilbert space4.14 The normal solvability of multiplication by a matrix function4.15 ?±-operators4.16 One-sided regularization of operators4.17 Projections of invertible operators4.18 ExercisesComments and references5 Local Principles and their first applications5.1 Localizing classes5.2 Multipliers on \$\$ \mathop l\limits^ \sim _p \$\$5.3 paired equations with continuous coefficients on \$\$ \mathop l\limits^ \sim _p \$\$5.4 Operators of local type5.5 ExercisesComments and referencesReferences.続きを見る http://hdl.handle.net/2324/1000045627 Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

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レコードID 3503564 Q1-390 50 Science (General). Science, general. ssj0001297923 9783764325848[3764325844](print) 9783034886475[3034886470] 2020.06.27 2020.06.28