Screen LibraryGeneralized analytic functions /
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| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Group Author: | ; ; |
| Published: |
Pergamon Press,
|
| Publisher Address: | Oxford ; New York : |
| Publication Dates: | 1962. |
| Literature type: | eBook |
| Language: |
English Russian |
| Series: |
International series of monographs on pure and applied mathematics ;
v. 25 |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780080096933 |
| Carrier Form: | 1 online resource (xxix, 668 pages) : illustrations. |
| ISBN: |
9781483184678 1483184676 |
| Access: | 3 Use copy |
| Index Number: | QA331 |
| CLC: | O174.5 |
| Contents: |
Front Cover; Generalized Analytic Functions; Copyright Page; ANNOTATION; Table of Contents; FOREWORD; PART ONE: FOUNDATIONS OF THE GENERAL THEORY OF GENERALIZED ANALYTIC FUNCTIONS AND BOUNDARYVALUE PROBLEMS; CHAPTER I. SOME CLASSES OF FUNCTIONS ANDOPERATORS; 1. Classes of functions and functional spaces; 2. Classes of curves and domains. Some properties of conformalmapping; 3. Some properties of Cauchy type integrals; 4 Non-homogeneous Cauchy-Riemann system; 5. Generalized derivatives in the Sobolev sense and theirproperties; 6. Properties of the operatorTg. 7. Green's formula for the class of functions D1p. Arealderivative8. On differential properties of functions of the form TGf. OperatorII; 9. Extension of the operatorII; 10. Some other properties of functions of the classes DZ(G)and D-Z(G; CHAPTEE II. REDUCTION OF A POSITIVE DIFFERENTIAL QUADRATIC FORM TO THE CANONICAL FORM. BELTRAMFS EQUATION. GEOMETRICAPPLICATIONS; 1. Introductory remarks. Homeomorphisms of a quadraticform; 2. Beltrami's system of equations; 3. Construction of the basic homeomorphism of Beltrami'sequation; 4. Proof of existence of a local homeomorphism. 5. Proof of the existence of a complete homeomorphism6. Reduction of a positive quadratic differential form to the canonical form Isometric and isometric-conjugate coordinatesystems on a surface; 7. Reduction of equations of elliptic type to the canonicalform; CHAPTER III. FOUNDATIONS OF THE GENERAL THEORY OFGENERALIZED ANALYTIC FUNCTIONS; 1. Basic concepts, terminology and notations; 2. Integral equation for functions of the class; 3. Continuity and differentiability properties of functions of theclass; 4. Basic lemma. Generalizations of some classical theorems. 5. Integral representation of the second kind for generalizedanalytic functions6. Generating pair of functions of the classDerivative in the Bers sense; 7. Inversion of the non-linear integralequation; 8. Systems of fundamental generalized analytic functions andfundamental kernels of tbe class; 9. Adjoint equation. Green's identity. Equations of thesecond order; 10. Generalized Cauchy formula; 11. Continuous continuations of generalized analytic functions. Generalized principle of symmetry; 12. Compactness; 13. Representation of resolvents by means of kernels. 14. Representation of generalized analytic functions by meansof generalized integrals of the Cauchy type15. Complete systems of generalized analytic functions. Generalized power series; 16. Integral equations for the real part of a generalizedanalytic function; 17. Properties of solutions of elliptic systems of equationsof the general form; CHAPTER IV. BOUNDARY VALUE PROBLEMS; 1. Formulation of the generalized Riemann-Hilbert problem. Continuity properties of the solution of the problem; 2. The adjoint boundary value Problem A '. Necessary and sufficient conditionsof solubility of Problem A. 3. Index of Problem A. Reduction of the boundary conditionof Problem A to the canonical form. |