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Krantz S.G. — Function theory of several complex variables
Krantz S.G. — Function theory of several complex variables



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Название: Function theory of several complex variables

Автор: Krantz S.G.

Аннотация:

This edition has been revised and updated to include two new chapters on recent developments in the field.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2001

Количество страниц: 579

Добавлена в каталог: 08.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Folland, G.B.      175
Forelli's theorem      96
Fornaess imbedding theorem      135 222 386
Fornaess — Krantz theorem      222
Fornaess, J.      9 13 141 168 222 421 462 476
Forstneric, F.      488
Forward light cone      161
Fourier, J., multiplier      205
Fourier, J., transform      203
Frankel, S.      479
Freeman, M.      241 314
Fridman, B.      10 454
Frobenius integrability theorem      311 312
Function, $C^{k}$ on a manifold      493
Function, $C^{\infty}$ on a manifold      493
Function, holomorphic on a manifold      493
Function, real analytic on a manifold      493
Fundamental solution      27 29 30
Fundamental solution for the Laplacian      37 114 203
Gain in regularity      464
Gamelin, T.W.      297
Gamma function of Euler      60
Garnett, J.      297 351
Gauss's lemma      275
Geometric type      464
Gilbarg, S.      143
Gleason, A.      69 227
Gleason, A., problem      13 422
Graded union      504
Graham, C.R.      112
Graham, I.      76 374 441 443
Graham, I., theorem      442
Grauert, H.      9 25 70 216 292 314 407 411 419
Green, G., function      42 43
Green, G., function for the ball      46
Green, G., theorem      35
Green, M.      476
Greene — Krantz theorem      454
Greene, R. E.      9 10 58 60 221 435 446 453 479
Greiner, P.      367 422
Guan, P.      470
Guilleman, V.      161
Hahn, K.T.      490
Hakim — Sibony approximation scheme      167 386
Hakim, M.      383
Hardy — Littlewood, lemma      411
Hardy — Littlewood, maximal function      324
Hardy — Littlewood, theorem      373
Hardy, G.H.      374
Hardy, G.H., class      302 321 339
Hardy, G.H., class, boundary limits for      321
Hardy, G.H., class, real variable theory of      351 376
Harmonic function      35
Harmonic function, maximum principle for      40 41
Harmonic function, mean value property for      39
Harmonic function, square of      70
Harmonic majorant      338 341
Harnack, inequalities      72
Harnack, principle      72
Hartogs, F.      8
Hartogs, F., domain      232
Hartogs, F., extension phenomenon      8 33 75 106
Hartogs, F., figure, generalized      292
Hartogs, F., figure, simple      291
Hartogs, F., functions      93 99
Hartogs, F., lemma      32 91
Hartogs, F., phenomenon      79
Hartogs, F., pseudoconvexity      143
Hartogs, F., triangle      169
Harvey, R.      73 241
Hatziafratis, T.      227
Hausdorff, F., measure      495
Hausdorff, F., topology on domains      59
Hefer's lemma      224 244
Heisenberg group      112
Henkin, G.M.      11 25 70 216 227 302 379 419 432 489
Henkin, G.M., integral formula      225
Henkin, G.M., integral solution in $\mathbb{C}^{2}$      408
Henkin, G.M., solution operator for the $\bar{\partial}$ problem      406
Henon map      476
Hermitian inner product      354
Hessian, complex      126
Hessian, real      120
Hilbert space      50 176
Hilbert space, with reproducing kernel      66
Hille, E.      362
Hironaka, H.      300
Hoermander, L.      9 175
Holomorphic convexity      240
Holomorphic curve      471
Holomorphic extension      318
Holomorphic function      4 31 32
Holomorphic function, constructing      17 25
Holomorphic function, fake      200
Holomorphic function, maximum principle for      40
Holomorphic function, removable set for      300
Holomorphic inverse      55
Holomorphic mapping with a fixed point      429
Holomorphic p-form      271
Holomorphic support function      138
Holomorphic vector field      466
Holomorphy, domain of      151
Homogeneity argument      122
Homogeneous coordinates      287
Hopf Lemma      49 73 461 489
Huckleberry, A.      432
Hull with respect to a family of functions      152
Hurwitz, A., theorem      76 310
Hyperbolicity      483
Hypoadmissible convergence      363
Hypoadmissible curve      377
Hypoellipticity, failure of      421
Ideal      275
Ideal, maximal      275
Ideal, sheaf      296
Imbedding      432
Implicit function theorem      3
Implicit function theorem, holomorphic      54
Increasing sums      179
Indeterminate point      282
Inequivalence of ball and poly disc      239 432 453
Inequivalence of Kobayashi metric and Bergman metric      482
Inequivalence of weakly and strongly pseudoconvex domains      433
Infinitesimal form of the canonical metrics on the ball      480
Inner function      381
Inner function, closure of      396
Inner function, existence of      395
Inner function, problem      382
Inner function, singular      382
Inner product for vector fields      505
Integral, divisor      282
Integral, domain      275
Integral, manifold      311
Integration on a manifold      506
Interior, estimates for the $\bar{\partial}$ problem      424
Interior, multiplication      36
Interior, product      501
Interpolation of operators      358
Invariance of finite type      491
Irreducible ring element      275
Isometries of the canonical metrics      438
Isometries, determined by first order behavior      444
Isotropic balls      352 356
Isotropy group      432
Iwasawa decomposition      113
Jacobian      53
Jacobian, complex      53
Jacobian, real      53
Jacobowitz, H.      423
Jensen inequality      328
Jewell, N.      233
John — Nirenberg theorem      376
Jones, P.W.      197 297
Jordan canonical form      444
Josefson, B.      98
Julia, G.      476
Karp, W.      430
Kashiwara, M.      161
Kawai, T.      161
Kelvin inversion      45
Kerzman — Rosay theorem      482
Kerzman, N.      13 59 70 168 216 331 407 411 419 423
Kim, K.T.      479
Kiselman, C.      462
Klembeck, P.      60
Klimek, M.      98
Kobayashi metric      365 371
Kobayashi metric, one disc      485
Kobayashi, S.      79
Kobayashi/Eisenman volume form      446
Kobayashi/Royden distance, integrated      482
Kobayashi/Royden distance, maximality of      440
Kobayashi/Royden length of a curve      437
Kobayashi/Royden metric      434 437
Kobayashi/Royden metric, isometries      487
Kodama, A.      479
Kohn global regularity theorem for the $\bar{\partial}$ problem      207 426
Kohn solution to the $\bar{\partial}$ equation      195
Kohn — Nirenberg domain      167
Kohn — Nirenberg example      140
Kohn, J.J.      9 129 175 314 422 427 463 470
Kontinuitaetssatz      144
Koppelman, W.      78
Koranyi, A.      354
KOREVAAR, J.      164
Koszul complex      239
Kra, I.      441
Krantz, S.G.      9 10 58 60 99 103 143 175 221 233 307 351 362 365—367 370 374 376 377 421 430 435 441 446 453 470 479 488
Krantz, S.G., estimates on the Kobayashi metric      486
Kugelsatz      8 291
Laplacian      35
Laplacian, self-adjoint ness of      204
Latter, R.      351
Lefschetz, S.      244 476
Lehto, O.      362
Lelong, P.      378
Lempert, L.      10 347 454 462
Lempert, L., theorem      442
Lempert, L., theorem, applications      443
Leray, J.      254
Leray, J., form      21
Leray, J., theorem      263
Levi, E., form      126 128 190 433
Levi, E., form, coordinate free definition      232
Levi, E., form, rank of      312
Levi, E., polynomial      216
Levi, E., problem      8 29 131 215
Levi, E., problem for complete circular domains      158
Levi, E., problem for tube domains      160
Levi, E., problem, consequences of      158
Levi, E., problem, solution of      215
Levi, E., pseudoconvex      128
Levi, E., pseudoconvex, strongly      128
Lewy — Pincuk reflection principle      207
Lewy, H.      423
Lieb, I.      25 70 216 407 411 419
Lindeloef principle      362 376
Lindeloef principle for hypoadmissible convergence      364
Lindeloef principle, failure for admissible convergence      363
Liouville theorem      114
Lipschitz, R., estimate for the $\bar{\partial}$ problem      415 416
Lipschitz, R., estimate for the $\bar{\partial}$ problem, exactness of      416
Lipschitz, R., space      365 411
Lipschitz, R., space, nonisotropic      366
Littlewood, J.E.      374
Local coordinates for studying the Henkin solution      409
Local Parametrization Theorem      471
Local ring      275
Local solvability      426
Localization of singularities      227
Locally finitely generated sheaf      293
Locally regularly presented manifold      295
Logarithm of a set      105
Logarithm, convexity      105
Lojaciewicz, S.      103 279
Lojaciewicz, S., theorem      491
Long $\mathbb{C}^{2}$      170
Long exact cohomology sequence      265 268
Low, E.      12 383 395
Lower semicontinuous function      81
Lu Qi-Keng      490
Lu Qi-Keng, conjecture      58
Ma, D.      10 351 377
MAIN GOAL      183
MAIN GOAL, MODIFIED      188
Manifold      493
Manifold, $C^{k}$      493
Manifold, $C^{\infty}$      493
Manifold, diffeomorphism of      493
Manifold, mapping of      493
Manifold, product of      494
Manifold, real analytic      493
Manifold, smooth      493
Manifold, union of      494
MAP      429
Mapping      429
Mapping, problem      59
Marcinkiewicz interpolation theorem      371
Marshall's theorem      395
Martin, W.      99
Maximal function, characterization of Hardy spaces      351
Maximal function, comparison of      351
McNeal, J.      141 475
Mergelyan theorem      14
Minkowski, H.      117
Minkowski, H., functional      124
Mittag-Leffler theorem      11 75 254
Model domain      438
Monge — Ampere equation      98
Morrey, C.B.      9 175
Moser, J.      10 60
Multi vector      504
Multi-covector field      504
Multi-index notation      3
Multiplicity of a holomorphic function      471
Nagel — Rudin theorem      372
Nagel, A.      13 354 470 475
Narasimhan, R.      9 314
Narasimhan, R., lemma      134 171
Nebenhuelle      142
Nevanlinna class      301 302 379
Nirenberg — Webster — Yang proof of Fefferman's theorem      489
Nirenberg, L.      129
Noell, A.      384
Noetherian ring      275
Non-continuable holomorphic function      7
Non-locally solvable operator      422
Non-smooth biholomorphic mapping      485 489 491
Non-uniqueness of Kobayashi/Royden extremals      489
Non-vanishing Jacobian of a biholomorphism      486
Nonisotropic balls      352 356
Nontangential approach region      324
Nontangential boundary limits for holomorphic functions      326 330 349
Nontangential boundedness and nontangential limits      348
Norguet, F.      8
Normal family      439 482
Normal function      376
Normal vector      118
Normalized complex tangential curve      366
Normalized holomorphic function      276
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