Mikhlin S.G., Prossdorf S. — Singular Integral Operators :: Электронная библиотека попечительского совета мехмата МГУ

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Mikhlin S.G., Prossdorf S. — Singular Integral Operators

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Название: Singular Integral Operators

Авторы: 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).

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1986

Количество страниц: 528

Добавлена в каталог: 11.11.2012

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Предметный указатель

$\alpha$ -homogeneous function      283
$\Phi$ -operator      22 34
$\Phi$ -problem      28
$\varepsilon$ -point collocation method      458
Abstract singular operator      73 432
Agranovich      21 263 266 277 340 369
Akilov      29 49 439 449
Aleksandrov, A.B.      111
Aleksandrov, P.S.      389
Aleksidze      424
Alexandroff      352 377
Algebra, $\mathds{R}$ -      84
Algebra, decomposing      84
Algebra, Wiener      84
Algebraic operator      196
Anisotropic condition      275
Anisotropic singular operator      283
Applicable approximation method      431
Applicable projection method      426
Approximate solution      426
Approximating equation      426
Approximation property      463
Arnold      451 459 460 461 463
Aronszajn      419
Atiyah      369 374
Atkinson      22 34
Aubin      453 459
Avrahamce      165
Aziz      463
Babuska      463
Bakelman      346
Basheleshvili      383
Bateman      287 296
Baxter      437
Beltrami operator      215
Besov      283
Betti's formula      384
Birman      283
Bitsadze      188 418
Boettcher      96 445 446
Boikov      444
Bojarski      115 117 187
Bony      52
Booss      369 374
Bounded subset      32
Boutet de Monvel      409
Brackx      419
Breuer      28
Budyanu      61 86 88 124
Burchuladze      383
Butzer      437 439
Calderon — Zygmund operator      315
Calderon, A.P.      52 70 245 247 249 261 267 268 277 278 280 281 301 305 409
Calderon, C.P.      52
Canonical factorization of a matrix function      119
Carleman shift      199
Carleson curve      57
Cartan      369
Cauchy integral operator      419 420
Cauchy kernel      45
Cauchy singular integral      45
Cauchy — Riemann system      187
Cauchy — Riemann system, generalized      187
Characteristic of a singular integral      321
Characteristic part of a singular operator      73
Characteristic polynomial      196
Characteristic root      196
Chebotarev      143
Cherski      74
Chikin      172
Clancey      102 124
Classical solution      34
Closed composite curve system      90
Closed curve system      44
Coburn      99 165
Coddington      180
Codimension      16
Coefficients of a paired operator      71
Coefficients of an abstract singular operator      73
Coifman      52 313—315
Cokernel      15
Coleman      316
Commutation formula      60
Compact operator      32
Compact part of a singular operator      73
Complementary projection      15
Completely continuous operator      32
Composite curve system      90
Compound generalized singular operator      406
Constant symbol      273
Convergence manifold      426 431
Convergent approximation method      431
Convex set      32
Cook      447
Corner point of a curve system      43
Costabel      140
Cotlar      52
Countable normed space      33
Curve of the class $C^{\infty}$       66
Dang      461
Danilyuk      52
David      52 57
Decomposing algebra      84
Deficiency      15
Degenerate symbol      81
Degree of a pseudo-differential operator      340
Delanghe      419
Dieudonne      24
Dikanski      28
Dini condition      209
Dini space      208
Direct complement      16
Direct sum      15
Dirichlet problem      185
distribution      35
Distribution, tempered      39
Dominant part of a singular operator      73
Double layer potential      384
Douglas      28 102 165 188
DOW      446
Dual paired operator      71
Duduchava      61 107 140 408
Duistermaat      409
Dunford      47
Dushkoy      439 441
Dybin      143 165
Dynin      369
Dzhishkariani      446
Elliott      446
Elschner      179—181 186 451 461—463
End point of a curve system      43
Equation of the second kind      19
Equivalent left regularizer      19
Equivalent operators      389 392
Equivalent right regularizer      20
Erdogan      447
Eskin      389 408
Essential norm      389
Essential supremum      257
Fabes      52
Factorization of a function      76 83 89
Factorization of a matrix function, canonical      119
Factorization of a matrix function, left      118
Factorization of a matrix function, right      118
Fedosov      23 26 369 374
Fefferman      313—316
Feldman      28 84 86 116 127 428 437 461
Fichera      81
Fichtenholz      69
Finite section method      437

fix      464
Fourier operator      345
Frechet space      32
Fredholm operator      22 36
Fredholm operator on the distribution space      36
Fredholm problem      28
Friedrichs      215 409
Fromme      446
Fuchsian differential operator      180
Fueter      419
Function of bounded mean oscillation      316
Fundamental sequence      389
Gabdulhaev      439 441 452
Gadzhiev      267
Gakhov      70 79 91 96 107
Gantmacher      148
Gaponenko      165
Garding inequality      461
Gegelia      232 234 347 383
Gelfand      33 35 38 84 168 270 286 323 397
General singular operator      299
Generalized analytic function      187 419
Generalized Cauchy — Riemann system      187
Generalized factorization of a function $a\in L_{\infty}(\Gamma)$ in the space $L_{p}(\Gamma,\varrho)$       100
Generalized factorization of a function a with respect to $\Gamma$       89
Generalized function      35
Generalized left zero divisor      397
Generalized Plemelj — Sokhotski formulae      420
Generalized Riemann — Hilbert problem      187
Generalized right zero divisor      397
Generalized singular integral operator      405
Generalized solution      35
Generating system of seminomas      32
Gerasoulis      446 461
Giraud      38 117 234 251 355
Glushko      180 210
Gohberg      25 26 28 52 55 57 61 62 66 74 79 81 83 84 86 88 91 96 102 103 107 111 117 124 127 133 134 137 138 140 165 306 322 325 427 428 437 461
Golberg      446 447
Goldberg      28
Gordadle      52
Grudski      165
Guerlebeck      424
Gupta      447
Haftmann      446
Haikin, M.I.      143 161 165 168
Haikin, Yu.E.      277 282 286 297 298 410
Halilov      74
Halmos      389
Hardy      56 284
Hausdorff      16
Havin      52
Heinig      124
Hermitean interpolation polynomial      145
Heunemann      97 107
hilbert      187
Hilbert kernel      63
Hilbert singular integral      62
Hilbert transform      56
Hoelder condition      44
Hoelder space      209
Hoermander      38 273 282 339 343 345 357 399 409 417
Homogeneous pseudo-differential operator      340 342
Homogeneous pseudo-differential operator of negative degree      340
Homomorphism      32
Homotopic operators      27
Hopf      352 377
Horvath      354
Hsiao      451 460
Hunt      313
Hurewicz      372
Ikegawa      461
Ilyin      283
Index of a function      76 79 104 107 109 139
Index of a function in the space $L_{p}(\Gamma,\varrho)$       100
Index of a problem      28
Index of a symbol matrix      369
Index of an equation      409
Index of an operator      15 36
Index of an operator, partial      118
Index of an operator, right      118
Index of an operator, sum      118
Index of an operator, total      118
Index, left      118
Integral operator with weak singularity      57
Inverse property      463
Inverse, left      27
Inverse, right      27
Invertible operator      27
Ioakimides      446
Itskovich      62 249 254
Ivanov      439 451 452
Jen      461
Jodeit      52
Journe      52 314 316
Junghanns      431 441 444 446 448 449 470
Kantor      346
Kantorovich      29 49 439 449 476
Karapetyants      143
Karpenko      447
Kato      26 28
Kernel of an operator      15
Kernel, Cauchy      45
Kernel, Hilbert      63
Kernel, Riesz      280
kernel, weakly singular      57
Khvedelidze      24 28 52 56 57 81 83 107 117 127 133 185
Khvoles      234 241 270 347 357
Kinoshita      383
Koehler      21 115 172
Koethe      25
Kohn      38 273 339
Kokilashvili      57
Kopp      31 188 190
Kosulin      172
Kozak      445 470
Krachkovski      28
Krasnoselski      57 431 483
Kravchenko      204
Krein, M.G.      25 26 28 86 124 138
Krein, S.G.      28
Krupnik      28 52 55 57 62 66 74 79 83 91 96 99 102 103 107 111 112 115 116 127 133 134 137 140 204 306 322 325 330
KRYLOV      476
Kupradze      383
Lame equation      383
Lavrentyev      452
Layer of charge potential      384
Left factorization of a matrix function      118
Left indices      118
Left inverse      27
Left invertible operator      27
Left regularization      17
Left regularizer      17
Leiterer      82 117
Length of a multiindex      150
Lerer      124
Levchenko      427
Leyinson      180
Limit of a function      149
Lindenstrauss      16
Linear dilation of an operator      135
Linear element of a manifold      347
Linear topological space      32
Lipschitz space      209
Littlewood      56 284
Litvinchuk      198 199 204
Lizorkin      283
Local left regularizer      393
Local right regularizer      393
Localization principle      389 445—443 459
Locally continuous operator family      394

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