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| Krantz S.G. — Function theory of several complex variables |
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| Предметный указатель |
Abel's lemma 101
Acyclic cohomology 266
Adjoint of the  operator 186
Adjoint of the operator, formal 190
Adjoint of the 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  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 problem 198
Canonical vs. Henkin solution for the 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  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  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 operator 403
Estimates for the operator on ellipsoids 421
Estimates for the operator, basic 192
Estimates for the operator, optimal 418
Estimates for the operator, sharp 464
Estimates for the operator, uniform 411
Euclidean Hartogs figure generalized 292
Euclidean space 1
Exhaustion function 191
Existence theorem for the 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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