The Riemann Boundary Problem on Riemann Surfaces: Mathematics and its Applications, cartea 16
Autor Y. Rodinen Limba Engleză Hardback – 31 ian 1988
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Specificații
ISBN-13: 9789027726537
ISBN-10: 9027726531
Pagini: 220
Ilustrații: XIII, 199 p.
Dimensiuni: 156 x 234 x 18 mm
Greutate: 0.49 kg
Ediția:1988
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and its Applications
Locul publicării:Dordrecht, Netherlands
ISBN-10: 9027726531
Pagini: 220
Ilustrații: XIII, 199 p.
Dimensiuni: 156 x 234 x 18 mm
Greutate: 0.49 kg
Ediția:1988
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and its Applications
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchCuprins
1. The Riemann Boundary Problem on Closed Riemann Surfaces.- §1. Riemann Surfaces.- §2. Functions and Differential Forms. Abelian Integrals and Differentials.- §3. Riemann Bilinear Relations. The Riemann — Roch Theorem.- §4. Cauchy-type Integrals.- §5. The Riemann Problem. Number of Solutions.- §6. Inversion of Abelian Integrals and Abel’s Theorem. Solvability of the Riemann Problem.- §7. Riemann Theta-Functions. Solvability of the Riemann Boundary Problem.- §8. Explicit Formulae for Solutions of the Riemann Problem.- 2. Complex Vector Bundles over Compact Riemann Surfaces.- §9. De Rham and Dolbeault Theorems.- §10. Divisors. Complex Vector Bundles. Serre and Riemann Theorems.- §11. The Riemann — Roch Theorem. The Riemann Problem.- §12. The Second Cousin Problem. Solvability of the Riemann Problem.- 3. The Riemann Boundary Problem for Vectors on Compact Riemann Surfaces.- §13. The Riemann Boundary Problem for Vector Functions.- 4. The Riemann Boundary Problem on Open Riemann Surfaces.- §14. Open Riemann Surfaces.- §15. D-Cohomologies.- §16. D-Divisors. The Second Cousin Problem.- §17. The Riemann Problem. Solvability.- §18. The Solving of the Riemann Problem in the Explicit Form.- 5. Generalized Analytic Functions.- §19. Bers — Vekua Integral Representations.- §20. The Riemann — Roch Theorem.- §21. Nonlinear Aspects of the Generalized Analytic Function Theory.- 6. Integrable Systems.- §22. The Schrödinger Equation.- §23. The Landau — Lifschitz Equation.- §24. Riemann — Hilbert and Related Problems.- Appendix 1 Hyperelliptic Surfaces.- Appendix 2 The Matrix Riemann Problem on the Plane.- Appendix 3 One Approximate Method of Solving the Matrix Riemann Problem.- Appendix 4 The Riemann — Hilbert Boundary Problem.- Notations.-References.
Recenzii
`This valuable book characterized by an original point of view in both choice and organization of the material, will be much appropriated by mathematicians and physicists and will favourably influence the future researchers.'
Zentralblatt für Mathematik, 695
Zentralblatt für Mathematik, 695