Boundary Value ProblemsCourier Corporation, 1990 M01 1 - 561 páginas A brilliant monograph, directed to graduate and advanced-undergraduate students, on the theory of boundary value problems for analytic functions and its applications to the solution of singular integral equations with Cauchy and Hilbert kernels. With exercises. |
Contenido
FUNCTIONS SATISFYING THE HÖLDER CONDITION | 5 |
OTHER GENERALIZED PROBLEMS | 18 |
LIMITING VALUES OF THE CAUCHY TYPE INTEGRAL INTEGRALS OVER | 20 |
PROPERTIES OF THE LIMITING VALUES OF THE CAUCHY TYPE INTEGRAL | 38 |
THE HILBERT FORMULAE FOR THE LIMITING VALUES OF THE REAL | 44 |
EXCEPTIONAL CASES AND THE GENERAL CONCEPT OF INDEX | 45 |
BEHAVIOUR OF THE CAUCHY TYPE INTEGRAL AT THE ENDS OF THE CON | 53 |
INTEGRAL OF THE CAUCHY TYPE AND POTENTIALS | 73 |
33 HISTORICAL NOTES | 284 |
VARIOUS GENERALIZED BOUNDARY VALUE PROBLEMS | 290 |
BOUNDARY VALUE PROBLEM OF RIEMANN TYPE WITH THE BOUNDARY | 316 |
of solving the problem 322 35 4 Singular integrodifferential equation | 324 |
regularizing factor 336 36 5 The solution of the homogeneous Hilbert | 352 |
36 INVERSE BOUNDARY VALUE PROBLEM FOR A MULTIPLYCONNECTED | 358 |
and integrodifferential equation 364 | 364 |
BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF ELLIPTIC EQUATIONS | 375 |
RIEMANN BOUNDARY VALUE PROBLEM | 85 |
EXCEPTIONAL CASES OF THE RIEMANN PROBLEM | 107 |
RIEMANN PROBLEM FOR MULTIPLYCONNECTED DOMAIN SOME | 113 |
RIEMANN BOUNDARY VALUE PROBLEM WITH SHIFT | 121 |
HISTORICAL NOTES | 137 |
SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNEL | 143 |
THE DOMINANT EQUATION | 157 |
FUNDAMENTAL PROPERTIES OF SINGULAR EQUATIONS | 171 |
EQUIVALENT REGULARIZATION THE THIRD METHOD OF REGULARIZATION | 178 |
EXCEPTIONAL CASES OF SINGULAR INTEGRAL EQUATIONS | 194 |
PROBLEMS ON CHAPTER III | 201 |
AND SINGULAR INTEGRAL EQUATIONS WITH HILBERT KERNEL | 207 |
REGULARIZING FACTOR | 213 |
THE HILBERT BOUNDARY VALUE FOR SIMPLYCONNECTED DOMAINS | 220 |
30 RELATION BETWEEN THE HILBERT AND RIEMANN PROBLEMS | 228 |
SINGULAR INTEGRAL EQUATION WITH HILBERT KERNEL | 236 |
BOUNDARY VALUE PROBLEMS FOR POLYHARMONIC AND POLYANALYTIC | 249 |
THE INVERSE BOUNDARY VALUE PROBLEM FOR ANALYTIC FUNCTIONS | 265 |
HISTORICAL NOTES | 398 |
BOUNDARY VALUE PROBLEMS AND SINGULAR INTEGRAL | 406 |
RIEMANN BOUNDARY VALUE PROBLEM FOR OPEN CONTOURS | 420 |
DIRECT SOLUTION OF THE RIEMANN PROBLEM | 428 |
RIEMANN PROBLEM FOR A COMPLICATED CONTOUR | 436 |
HILBERT BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS COEFFICIENTS | 449 |
THE DOMINANT EQUATION FOR OPEN CONTOURS | 462 |
COMPLETE EQUATION FOR OPEN CONTOURS | 472 |
THE GENERAL CASE | 480 |
PROBLEMS ON CHAPTER VI | 487 |
INTEGRAL EQUATIONS SOLUBLE IN CLOSED FORM | 494 |
SOME TYPES OF INTEGRAL EQUATIONS WITH POWER AND LOGARITHMIC | 526 |
HISTORICAL NOTES | 544 |
73 | 552 |
| 559 | |
| 560 | |
| 561 | |
Términos y frases comunes
adjoint analytic function arbitrary constants boundary condition boundary value problem canonical function Cauchy kernel Cauchy type integral class of functions closed contour complex conditions of solubility conformal mapping Consequently considered curve deduced defined denote density derivatives determined Dirichlet problem domain D+ dominant equation equivalent Fredholm equation Fredholm integral equation function analytic function F(z G₁(t given Hence Hilbert boundary value Hilbert problem Hölder condition homogeneous problem I. N. Vekua ib(s infinity integral representation investigation L₁ limiting values method multiply-connected domain non-homogeneous problem number of solutions obtain plane pole polynomial prove reduced regularizator regularizing factor relation Riemann boundary value Riemann problem right-hand side satisfies Hölder's condition satisfies the Hölder single-valued singular equation singular integral equation Sokhotski formulae solution of equation solving theorem theory unit circle vanish variable X+(t zero ατ πί ди