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Mikhlin S.G., Prossdorf S. — Singular Integral Operators
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Название: Singular Integral OperatorsАвторы: Mikhlin S.G., Prossdorf S. Аннотация: The present edition differs from the original German one mainly in the following additional material: weighted norm inequalities for maximal functions and singular operators (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with discontinuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles).
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1986Количество страниц: 528Добавлена в каталог: 11.11.2012Операции: Положить на полку |
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Locally convex space 32 Locally Fredholm operator at a point 393 Lopatinski condition 188 Lorenz 411 417 Lounesto 419 Luzin 52 Lyapunov condition 43 Lyapunov curve 43 Lyapunov curve system 43 Lyapunov curve system, piecewise 43 Magnaradze 177 Major part of the symbol 341 Mandzhavidze 117 127 Marcus 454 Markus 28 82 116 Maximal function 313 Mazya 277 282 298 357 410 414 416 McIntosh 52 Mean derivative of order n 149 Meister 187 Meyer, Ch. 196 204 205 Meyer, S. 158 204 Meyer, Y. 52 314 316 Mickenhoupt 313 314 Mikhailov 284 Mikhailova-Gubenko 220 263 266 270 347 357 Mikhlin 21 24 38 39 47 52 58 60 70 81 82 117 211 214 215 220 222 238 239 244 251 257 261 266 267 303 318 319 330 332 335 337 347 354 369 371 375 378 382 383 430 441 442 453 476 477 478 Minc 454 Miranda 188 311 355 Modulus of continuity 208 Mttlthopp 452 Muhammed-Naser 419 Muller 424 Multidimensional analogue of the Cauchy singular integral operator 420 Multidimensional singular integral 221 Multiindex of dimension r 150 Multiplicity of a system of zeros 146 Mura 383 Muskhelishvili 31 47 49 61 68 69 79 107 117 124 127 177 183 186 189 191 192 195 Natanson 449 Nedelec 451 Nessel 437 439 Nettmark 389 Neumann problem 185 Nied 470 Nikolski, S.M. 357 Nikolski, Yu.S. 285 Nirenberg 38 188 273 339 Node 475 Node, supporting 475 Nodes of a curve system 43 Noether 22 79 83 Noether theorems 83 Norm 33 Norm, essential 389 Normable space 33 Normally solvable in generalized functions 36 Normally solvable operator 16 Normally solvable problem 28 Normed space 33 Norrie 461 Nuclear operator 26 Nullity 15 Nyaga 140 Operator of local type 389 Operator of normal type 73 81 Operator of Wiener — Hopf type 71 Operator, abstract singular 73 Operator, algebraic 196 Operator, anisotropic singular 283 Operator, Beltrami 215 Operator, Calderon — Zygmund 315 Operator, compact 32 Operator, completely continuous 32 Operator, dual paired 71 Operator, equivalent 389 Operator, equivalent at a point 392 Operator, Fourier 345 Operator, Fredholm 22 Operator, Fuchsian differential 180 Operator, general singular 299 Operator, homo topic 27 Operator, invertible 27 Operator, left invertible 27 Operator, locally Fredholm 393 Operator, maximal 313 Operator, normally solvable 16 Operator, nuclear 26 Operator, paired 71 Operator, polysingular 336 Operator, pseudo-differential 273 339 Operator, right invertible 27 Operator, semi-Fredholm 22 Operator, simple singular 299 Operator, singular 73 Operator, smoothing of order l 304 Operator, strongly elliptic 453 462 Operator, transposed 82 Operator, transposed paired 71 p, 104 107 p, 104 107 p, 109 p, 109 p-index of a function 104 p-regular function 104 Paired operator 71 Pairwise coordinated system of seminorms 33 Palais 28 369 374 Partial indices 118 Partial multiplicaties of a system of zeros 148 Pascali 187 188 Peetre 267 Pereyra 285 Perlin 475 476 Peterhaensel 408 Pham The Lai 476 Piecewise Lyapunov curve system 43 Pietsch 25 34 Plamenevski 286 345 410 414 416 Plemelj 47 48 Poincare problem 185 Pole of a singular integral 321 Polya 284 Polygonal method 452 Polyharmonic potential 258 Polynomial, characteristic 198 Polysingular integral operator 336 Power 165 Privalov 50 61 64—66 234 Problem of the oblique derivative 185 Proessdorf 21 28 34 39 61 70 74 82 83 88 114 124 143 145 150 154 156 158 161 163 165 168 172 179 180 188 189 192 193 417 422 426 428 431 432 437—441 451—453 459—462 465 468—472 478 Projection 15 Projection equation 426 Projection method 426 Projection of L onto 16 Przeworska-Rolewicz 28 74 196 Pseudo-differential operator 273 339 Pseudo-differential, homogeneous 340 342 R-algebra 84 Radeva 477 Radon curve 52 Raikov 38 84 270 323 397 Rathsfeld 444—446 451 452 460 461 465 470 472 Regular functional 35 Regular point of a curve system 43 Regularization of an equation 19 Regularization, left 17 Regularization, right 17 Regularization, two-sided 17 Regularizer, equivalent left 19 Regularizer, equivalent right 20 Regularizer, left 17 Regularizer, local left 393 Regularizer, local right 393 Regularizer, right 17 Rempel 369 374 Riemann sphere 208 Riemann — Hilbert problem 183 Riemann — Hilbert, generalized 187 Riesz kernel 280 Riesz — Schauder equation 19 Riesz, F. 278 Riesz, M. 47 52 280 Right factorization of a matrix function 118 Right indices 118 Right inverse 27 Right invertible operator 27 Right regularization 17 Right regularizer 17 Riviere 52 Robertson, A.P. 16 Robertson, W. 16 Rochberg 316 Rode 239 Rodman 124 Rogozhin 172 Rolewicz 28 74 Root, characteristic 196 Rozin 283 301 Ruzmetow 232 Saak 418 Saginashvili 165 Salayev 241 Samko 284 Saranen 451 459 Sarason 165 Schaefer 34 418 Schechter 28 Schmidt 439 451 452 453 459 463 466 471 472 Schueppel 163 Schulz 469 Schulze 369 374 409 Schwartz, J.T. 47 Schwartz, L. 39 224 Seeley 225 306 319 322 323 324 339 345 346 348 369 374 375 Seichuk 443 Seifert 352 Sementsul 96 143 156 165 Semi-Fredholm operator 22 Seminorm 32 Senichkin 345 Shamir 107 134 Shelepov 52 Shevchenko 357 363 Shilov 33 35 38 84 86 168 270 286 323 397 Shubin 339 345 409 Silbermann 21 74 96 115 124 144 156 158 161 163 165 168 171 172 180 204 426 428 431 432 437—441 444—446 448 449 468—471 Simonenko 81 88 99 102 117 127 128 133 239 398 402 Simple singular operator 299 Singer 369 374 Singular integral 45 221 Singular integral operator on a curve system 74 80 Singular integral operator with Carleman shift 199 Singular integral operator, generalized 405 Singular integral, Cauchy 45 Singular integral, Hilbert 45 Singular matrix operator 368 Singular operator 73 348 Singular operator with constant symbol 273 Singular operator, compound generalized 406 Singular support of a function 94 Slobodetski 413 Smirnov 66 68 Smoothing of order I 304 Sobolev 66 210 211 214 250 258 263 335 Sobolev — Slobodetski space 209 Sofronov 452 Sokhotski 47 Soldatov 112 Solomyak 283 Solution of a problem 28 Somiglian's tensor 384 Sommen 419 Space, countable normed 33 Space, Dini 208 Space, Frechet 32 Space, Hoelder 209 Space, linear topological 32 Space, Lipschitz 209 Space, locally convex 32 Space, normable 33 Space, normed 33 Space, Sobolev — Slobodetski 209 Spherical functions of order n 215 Sproessig 418—424 Srivastav 461 Steenrod 346 Stein 244 284 313 315 316 415 419 Steklov mean function 148 Stephan 460 Stereographic projection 207 Sternberg 346 Strang 464 Strongly elliptic operator 453 462 Sttberty 419 Sum index 118 Support of a function, singular 94 Supporting node 475 Supremum, essential 257 Symbol determinant of a singular matrix operator 118 249 368 Symbol matrix of a singular matrix operator 249 Symbol of an operator 36 81 132 133 134 139 247 257 272 405 Symbol ring 36 Symbol, constant 273 Symbol, degenerate 81 System of zeros 146 Sz.-Nagy 278 T-operator 419 Taibleson 357 Tangential plane to the manifold 347 Taylor derivative 144 Teichmann 163 Tempered distribution 39 Test function space 35 Theocaris 446 Thomas 451 461 465 Threlfall 352 Timan, A.F. 361 Timan, T.A. 238 Titchmarsh 307 Total index 118 Tovmasyan 176 Trace of an operator 22 26 Transposed operator 82 Transposed paired operator 71 Treves 409 Tricomi 222 244 Tricomi equation 204 Two-sided regularization 17 Tzafriri 16 Unger 123 124 Vainikko 431 477 483 Vasilevski 408 Vektta, I.N. 183—189 419 Vekua, N.P. 117 124 127 133 177 185 Verbitski 111 445 Vichnevetsky 446 Vilenkin 289 Vishik 340 354 389 408 Vladimirov 336
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