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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
Abel's lemma      101
Acyclic cohomology      266
Adjoint of the $\bar{\partial}$ operator      186
Adjoint of the $\bar{\partial}$ operator, formal      190
Adjoint of the $\bar{\partial}$ operator, operator      177
Admissible approach region      356
Admissible convergence for holomorphic functions      354
Admissible limits for holomorphic functions      360
Admissible limits re-examined      362
Admissible regions      353
Admissible set for the Kobayashi/Royden metric      440
Affinity function      250 259
Aleksandrov, A.B.      12 383 397
Alexander, H.      439
Alexander, H., Rudin's generalization      480
Alexander, H., theorem      480
Almost analytic extensions      424
Analytic continuation      14 242 318
Analytic convexity      241
Analytic disc      136
Analytic polyhedron      160 166 483 484
Analytic sheaf      293
Analytic space      131
Analytic type      466 467
Analytic, closed      136
Andreotti, A.      9 175 292
Approximation of a holomorphic function      14 419
Approximation theory      236
Artinian ring      275
Ascoli — Arzela theorem      45
Atlas      493
Automorphism group of $D^{n}$      431
Automorphism group of a domain      429
Automorphism group of the ball      70 480
Automorphisms of bounded circular domains      430
Bagemihl — Seidel theorem      349 373
Baire category theorem      108
Baire class      33
Banach — Alaoglu theorem      322
Barbell domain      242
Barker, S.R.      358
Barrett, D.      462
Basener, R.      141 170
Basin of attraction      477
Beatrous, F.      233
Bedford, E.      97 98 141 161 479
Behnke — Stein theorem      158
Bell, S.      59 70 455 462
Bell, S., lemma      457
Berg, C.      73
Bergman — Bell projection formula      459
Bergman, S.      49
Bergman, S. and Hardy spaces      307
Bergman, S. and Kobayashi/Royden metrics, incomparability of      491
Bergman, S., distance      56
Bergman, S., kernel      49
Bergman, S., kernel for the ball      62
Bergman, S., kernel, calculation of      76
Bergman, S., kernel, extremal property of      57
Bergman, S., kernel, transformation under a mapping      55
Bergman, S., kernel, uniqueness of      51
Bergman, S., metric      56 434
Bergman, S., metric for the ball      63
Bergman, S., metric, definiteness of      79
Bergman, S., metric, dominates the Caratheodory metric      490
Bergman, S., metric, geodesic of      65
Bergman, S., metric, isometry of      56
Bergman, S., projection      52
Bergman, S., space      50
Bergman, S., space, basis for      79
Besicovitch's theorem      103
beta function      61
Betti numbers      136
Biholomorphic inequivalence of the ball and the polydisc      65
Biholomorphic mapping      9 55 429
Biholomorphic mapping of finite type domains      475
Bishop, E.      314
Blank, B.      441
Blaschke, W., condition      328 379
Blaschke, W., factorization      327
Blaschke, W., product      12 381
Boas, H.      58 59
Bochner — Martinelli form      291
Bochner — Martinelli formula      22
Bochner — Martinelli kernel      30
Bochner, S.      49 99
Bochner, S., extension phenomenon      210
Bogoliubov, N.      161
Bonneau, P.      227
Bonneson, T.      117
Borel's theorem      103 256 469
Boundary values, specifying      396
Bounded linear operator      176
Bounded mean oscillation, function of      374 377
Boutet de Monvel, L.      59 68 70 234
Branched covering      300
Braun — Karp — Upmeier linearization theorem      430
Braun, R.      430
Bremerman, H.      8 99
Bungart, L.      69 227
Burbea, J.      490
Burns, D.      9 430 435 453 454
Calderon, A.P.      348
Calderon, A.P., theorem      349
Campbell — Baker — Hausdorff formula      311
Canonical factorization      12 329 382
Canonical kernels vs. constructible kernels      70
Canonical metrics on the polydisc      483
Canonical solution to the $\bar{\partial}$ problem      198
Canonical vs. Henkin solution for the $\bar{\partial}$ problem      406
Caratheodory construction      495
Caratheodory distance      436
Caratheodory distance, minimality of      441
Caratheodory isometries      487
Caratheodory metric      434 435
Caratheodory theorem      371
Caratheodory volume form      446
Caratheodory — Cartan — Kaup — Wu theorem      444
Carleson, L.      297
Cartan, H.      254 429
Cartan, H., formula      232 314 508
Cartan, H., theorem      429
Cartan, H., theorem A      293 295
Cartan, H., theorem B      293 295
Catlin, D.      384 464 470
Catlin, D., subellipticity theorem      475
Cauchy — Fantappie formula      77 226 407
Cauchy — Riemann equation      15
Cauchy — Riemann equation with non-smooth solution      194
Cauchy — Riemann equation without closed range      212
Cauchy — Riemann equation, inhomogeneous      15 25 27 28 34
Cauchy, A.      117
Cauchy, A., estimates      104
Cauchy, A., formula for the poly disc      31
Cauchy, A., integral formula      20 24
Cayley transform generalized      112
Cegrell, U.      98
Chain homotopy      31 260
Chain rule      76
Chang, D.C.      470
Chebycheff's inequality      324
Chern class      285
Chern map      285
Chern — Moser invariants      453
Chern, S.S.      10 60
Chirka, E.      362 365
Christ, F.M.      470 475
Cima, J.      307 362 365 376 488
Circled set      104
Circular domain      104
Closed operator      177
Closure of adjoint operator      178
Closure of range lemma      179
Coboundary      257
Coboundary, operator      257 290
Cochains      256
Cocycles      257
Coherent analytic sheaf      294
Cohomologous      259
Cohomology group      290
Cohomology of slices      286
Combinatorial topology      243
Common refinement      262
Commutator      466
Compactly divergent subsequence      439
Comparability of canonical metrics and Euclidean metric in the interior      487
Comparison domains, method of      331
Complete circular domain      104
Complete Reinhardt domain      104
Completeness of the canonical metrics      482 483 488
Complex affine space      94
Complex analytic dynamics      476
Complex foliation      485
Complex line      94
Complex manifold      295
Complex normal      465
Complex normal curve      372
Complex projective space, cohomology of      287
Complex structure tensor      124
Complex tangent space      125 355
Complexification      103
Condition r      455 462 475
Cone      161 324
Conjugate holomorphic vector field      466
Connecting morphism $\delta^{*}$      265
Constant sheaf      256
Continuously differentiable      3
Convex function      81 114
Convex set, geometrically      117
Convex, strongly      120
Convexifiability      136
Convexity      9 117
Convexity and domains of holomorphy      156
Convexity, affine sphere characterization      131
Convexity, analytic      120
Convexity, hyperplane characterization      164
Convexity, strict      130
Convexity, strong      130
Convexity, with respect to a family of functions      129
Convolution of forms      30
Convolution of two functions      26
Coordinate chart      493
Coordinate pair      493
Cordoba, A.      357
Corona problem      297 298
Corona theorem      297
Cotangent vector      504
Counting zeros of a holomorphic function      308
Cousin problem      12
Cousin problem, first      247
Cousin problem, first, for $C^{\infty}$ functions      247
Cousin problem, first, solution      247
Cousin problem, first, with bounds      418
Cousin problem, second      247
Cousin problem, second, application      253
Cousin problem, second, for meromorphic functions      283
Cousin problem, second, non-solvability of      250
Cousin problem, second, solution      249
CoverIng by geometrically simple subdomains      341
Covering, lemma      323
Cumenge, A.      421
Currents      30
D'Angelo, J.      423 464 470 488
D'Angelo, J., decomposition of a defining function      474
Dales, H.G.      241
Davie, A.M.      233
de Rham theorem, holomorphic      273 274
de Rham theorem, real      272
Defining function      3 71 117
Defining function, pullback of      172
Demailly, J.P.      9
Diaz, R.      307
Diederich, K.      168 421 462
Differential form      3 19 504
Differentials      2
Direct limit      259
Dirichlet problem      43
Distance decreasing properties of canonical metrics      438
Distance function      142
Distance function, smoothness of      164
distribution      27 201
Distribution, function      349
Divergence      37
Divisor      11 282
Dixon, P.      170 479
Dolbeault, P., complex      268
Dolbeault, P., isomorphisms      287
Dolbeault, P., theorem      268
Domain      3
Domain of boundedness for a power series      104
Domain of convergence for a power series      13 104
Domain of convergence, characterization of      106
Domain of holomorphy      6
Domain of holomorphy, characterization of      131 153
Domain, algebra, prescribing boundary values in      401
Douglas, R.      233
Edge-of-the-wedge theorem      161 162 166
Ehrenpreiss, L.      9 33
Eilenberg — MacLane spaces      292
Envelope of holomorphy      240 318
Epstein, B.      73
Equivalence of geometric and analytic type      469
Essential point      153
Essential point, locally      157
Esterle, J.      170 479
Estimates for the $\bar{\partial}$ operator      403
Estimates for the $\bar{\partial}$ operator on ellipsoids      421
Estimates for the $\bar{\partial}$ operator, basic      192
Estimates for the $\bar{\partial}$ operator, optimal      418
Estimates for the $\bar{\partial}$ operator, sharp      464
Estimates for the $\bar{\partial}$ operator, uniform      411
Euclidean Hartogs figure generalized      292
Euclidean space      1
Exhaustion function      191
Existence theorem for the $\bar{\partial}$ operator      194
Extension of an analytic function      14 213
Exterior derivative      507
Exterior differential operator      20
Exterior, product      500
Faa de Bruno      113 459
Factoring, holomorphic functions      12 310
Faran, J.      488
Farkas, H.      441
Fatou — Bieberbach domain      170 476
Fatou, P.      476
Federbush, P.      97
Federer, H.      495
Fefferman, C.      10 59 60 68 70 351 354 357 376 441 443 453 470
Fefferman, C., lemma      171
Fefferman, C., theorem      210 377 462
Fenchel, W.      117
Fermat, P.      117
Finite 1-type      472
Finite analytic type      468
Finite geometric type      468
Finite type      470 472
Finite type 2, genericity of      491
Finsler metric      434
Fisher, S.      441
Foliation      310 312 433 486
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