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Generalized analytic functions /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Oxford ; New York :
Pergamon Press,
1962.
|
| Colección: | International series of monographs in pure and applied mathematics ;
v. 25. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.