22. Complex analysis in probability theory

Kapitel in diesem Buch

1. Frontmatter 1
2. Prefatory note 5
3. From the editors 7
4. Contents 9
5. Introduction 13
6. I. Complex analysis and its relations to other spheres in mathematics
7. 1. Classical and modern methods of complex analysis 15
8. 2. Value distribution theory 59
9. 3. Polyanalytic functions 68
10. 4. Cohomological methods in complex analysis 85
11. 5. Connections between complex and global analysis: some analytical and geometrical aspects of the Riemann-Hilbert transmission problem 97
12. 6. On some complex-analytic methods in differential geometry 111
13. 7. Complex methods in the theory of infinitesimal bending of a surface 124
14. 8. Approximation methods for solving singular integral equations 131
15. II. Complex methods in partial differential equations and other applications of complex analysis
16. 9. Ordinary differential equations in the complex domain 142
17. 10. Boundary value problems for analytic and generalized analytic functions 150
18. 11. Elliptic systems in the plane 166
19. 12. Recent results and developments in generalized hyperanalytic function theory 174
20. 13. Complex methods in the theory of boundary value problems with respect to systems of partial differential equations of composed type 185
21. 14. Differential operators in the theory of elliptic equations and boundary value problems 198
22. 15. Solving of linear partial differential equations by using complex integral transforms 215
23. 16. Function theory in algebras 225
24. 17. Analytic continuation of solutions to partial differential equations with applications to problems in scattering theory 238
25. 18. Numerical methods for boundary value problems of elliptic systems in the plane 249
26. 19. Optimal control problems with elliptic differential equation systems of first order in the plane 270
27. 20. Methods of the theory of analytic functions in the theory of elasticity 280
28. 21. Some applications of generalized analytic functions in the shell theory 296
29. 22. Complex analysis in probability theory 309
30. Bibliography 339
31. Author index 387
32. Subject index 393