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| Krantz S.G. — Function theory of several complex variables |
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| Предметный указатель |
Normally convergent sequence 439
Oka, K. 8
Oka, K., coherence theorem 295
Oka, K., extension theorem 286
Oka, K., map 237
Oka, K., principle 249
Open ball 2
Order of a holomorphic function 275
Order of contact of an analytic disc 462
Orientation 37
Osculating balls 331
Osgood, W.F. 75
Outer function 382
Outward normal vector 4
Over-determined system 175
Ovrelid, N. 13 216 407 411
Paley — Wiener theory 164
Pang, M.Y. 443
Parabolic approach 353
Parks, H. 99 103 143
Partial differential operators 1
Partition of unity 4
Peak function 140 212 241 385
Peak function, smoothly varying 216
Peak interpolation set 234
Peak point 141 488
Peak set 234
permutations 180
Perron method 43
Picard, E., existence and uniqueness theorem 310
Picard, E., theorem 476
Pincuk, S. 479
Pluriharmonic function 94
Pluriharmonic function as the real part of a holomorphic function 95
Pluriharmonic function, differential characterization 94
Plurisubharmonic exhaustion 314
Plurisubharmonic exhaustion, bounded 168
Plurisubharmonic strictly 97
Plurisubharmonicity, locality of 97
Poincare — Bergman distance 436
Poincare — Bergman metric for the disc 63
Poincare, H. 10 453
Poincare, H., lemma 95 270
Poincare, H., metric 484
Poincare, H., problem, strong 284
Poisson — Szegoe kernel 67
Poisson — Szegoe kernel and solution of a Dirichlet problem 111
Poisson — Szegoe kernel for the ball 69
Poisson, S.-D., integral for the ball 48
Poisson, S.-D., integral, formula 43
Poisson, S.-D., kernel for the ball 46
Poisson, S.-D., kernel, lower bound for 332 334
Poisson, S.-D., kernel, uniqueness of 49
Poisson, S.-D., kernel, upper bound for 337
Polking, J. 73
Polydisc 2
Polynomial, convexity 238
Polynomial, hull 173
Power series 13 99
Power series, calculating the coefficients of 102
Power series, convergence of 99
Power series, expansion 32
Prime ring element 275
Principal divisor 283
Principal ideal domain 275
Proper holomorphic mappings of balls 488
Proper mapping 151 296 429 432
Pseudoconvex domain, intersection of 150
Pseudoconvex domain, planar 129
Pseudoconvex domain, union of 151
Pseudoconvex neighborhood systems 142
Pseudoconvexity, characterization of 144
Pseudoconvexity, locality of 151
Pseudoconvexity, strong Levi 132
Pseudoconvexity, weak Levi 132
Pseudodifferential operator 205
Pseudohyperbolic distance 65
psh functions 97
Pullback of a curve 472
Radial boundary limits 326
Radial boundary limits for harmonic functions 344
Radial limits for holomorphic functions 347
Ramadanov's theorem 78
Ramirez, E. 25 70 216 407
Range, R.M. 9 78 168 176 227 423
Rank of the Levi form 173
Rank theorem 486
Real analytic function 100
Real analytic function, differentiation of 101
Real analytic function, zero set of 102
Reducible element of a ring 275
Regular type of a point 472
Regularly imbedded  manifold 71
Regularly imbedded submanifold 494
Reinhardt domain 104
Relatively prime germs 281
Rellich lemma 204
Remmert, R. 9 432
Representative domains 49
Resolution of groups 264
Resolution of singularities 300
Resultant of polynomials 298
Riemann, B., mapping theorem 10 58
Riemann, B., metric 435
Riemann, B., spread domains 316
Riesz — Fischer theorem 52
Riesz, M., decomposition 378
Riesz, M., representation theorem 50
Right inverse for  5 201
Ring of germs of meromorphic functions 282
Rodin, B. 455
Roman, S. 459
Rosay, J.P. 170 354 475 479
Rothschild, L. 464
Royden, H. 443
Royden, H., lemma 489 490
Rudin, W. 11 161 170 301 302 307 370 373 382—384 479
Runge, K., approximation property 229
Runge, K., domain 239 481
Runge, K., property 229 231
Runge, K., theorem 14
Ryll — Wojtaszczyk polynomials 383
Sard's theorem 149
Schur's lemma 72
Schwartz, L., distribution 203
Schwartz, L., space 203
Schwarz, H.A., lemma 430 436
Second fundamental form 120
Semi-continuity of finite type 491
Semi-exact sequence 257
Semmes, S. 10
Separate analyticity 107
Series, summation methods 100
Serre, J.P. 33 254
Set of uniqueness 318
Sheaf 12 254
Sheaf of germs of  functions 255
Sheaf of germs of holomorphic functions 256
Sheaf of groups 254
Sheaf of modules 254
Sheaf of relations 294
Sheaf of rings 254
Sheaf, cohomology 256 257
Sheaf, fine 258
Sheaf, global sections of 262
Sheaf, projection 254
Sheaf, section of 254
| Sheaf, stalk of 254
Sheng, G. 354
Shirkov, D. 161
Shnider, S. 9 435 453 454
Sibony, N. 13 136 141 194 297 383 423
Sibony, N., counterexample to the corona theorem 372
Siegel, C.L. 276
Siegel, C.L., domain 112 160 173
Silhouette of a point 101
Silhouette of a set 101
Silov boundary 141 171
Simplicial cohomology 288
Singular cohomology 288
Singular function of Henkin 218
Siu, Y.T. 9 131 227
Sjoestrand, J. 59 68 70
Skoda, H. 9 11 176 302 379
Skwarczynsi, M. 58
Skyscraper sheaf 255
Smith, K.T., axioms 357
Smooth boundary 3
Smooth bounded domain with transitive automorphism group 447
Smooth continuation of a conformal mapping 7
Smooth dependence of solutions on data 220
Snake lemma 266
Sobolev, S.L., imbedding theorem 196
Sobolev, S.L., imbedding theorem on domains 204
Sobolev, S.L., space 196 197 202
Spencer, D.C. 175
Stability result for the problem 415
Stein, E.M. 37 70 164 348 351 354 358 367 373 376 407 422 464 470 475
Stein, E.M., lemma 339
Stein, E.M., theorem 367
Stein, K. 9 432
Stein, K., manifolds 314
Stein, K., manifolds, imbedding of 314
Stensones, B. 384
Stokes's theorem 19 20
Stolz region 324
Stout, E.L. 297
Strongly pseudoconvex domain with noncompact automorphism group 448
Subelliptic system of partial differential equations 418
Subharmonic function 83
Subharmonic function and the Laplacian 88 90
Subharmonic function, characterizations of 83
Subharmonic function, integrability of 86
Subharmonic function, removable sets for 91
Sublinear operator 358 371
Subsimplex 289
Suffridge, T. 488
Suita, N. 58
Support of a form 25
Surface measure by way of coordinate charts 496
Surface measure by way of fattening up 496
Surface measure for a parametrized surface 496
Szegoe, G. 49
Szegoe, G., kernel 66
Szegoe, G., kernel for the ball 69
Tangent bundle 504
Tangent space 503
Tangent vector 118 503
Tangential Cauchy — Riemann equations 210
Tangential vector field 467
Taut but not complete hyperbolic 483
Taut domain 482 485
Taylor, B.A. 98
Taylor, B.A., theorem 77
Tensor product 499
Toeplitz operator 233
Tomato can principle 168 240
Torus, solid 132
Totally geodesic submanifold 486
Totally real manifold 319 371 378 380
Treves, F. 423
Trudinger, N. 143
Truncated wedge domain 161
Tube domain 160 172 314
Tubular neighborhood 366
Type of a point 472
Type, geometric 468
Type, modules 467
Unbounded linear operator 176
Uniformization theorem 10
Unique factorization domain 275
Unit disc 3 321
Upmeier, H. 430
Upper semicontinuity of the type concept 474
Upper semicontinuous function 81
Valuation 275
Variety, analytic 471
Variety, irreducible 471
Variety, type of a curve 472
Variety, type, vs. regular type 473
Varopoulos, N.Th. 11 302
Vector bundle 504
Venugopalkrishna, U. 234
Vertex 289
Vesentini, E. 175
Virtanen, K.I. 362
Vitushkin, A. 382
Vladimirov, V. 123
Volume form 2
Volume of the unit ball 61
Wainger, S. 354 475
Warschawski, S. 455
Weak boundedness of the Hardy — Littlewood maximal function 324
Weak derivative 180
Weak exterior differentiation 180
Weak type, boundedness of the maximal function 346
Weak type, function 324
Weak type, operator 324
Weakly pseudoconvex domain as the union of strongly pseudoconvex domains 158
Webster, S. 488
Wedge product 500
Weierstrass, K., division theorem 278
Weierstrass, K., polynomial 276
Weierstrass, K., preparation theorem 276
Weierstrass, K., theorem 11
Weight functions 185
Weighted  space 182 183
Weighted Sobolev spaces 175
Weil, A. 270
Weil, A., domains 159
Weiss, G. 37 164
Wells, R. 9 435 453 454 465
Wermer, J. 13
Wermer, J., example 482
Weyl's lemma 42 200
Whitney, H. 495
Whitney, H., decomposition of an open set 111
Widman, K.O. 348
Wiegerinck, J. 58 96 110 115 164 421
Wiener covering lemma 345
Wolff, T. 297
Wong — Rosay theorem 447
Wong, B. 479
Wong, B., lemma 447
Wong, P. 443
Worm domain 142 170
Wright, J.D.M. 176
Wu, H.H. 430 440 482
Yamada, A. 58
Yau, S.T. 430
Yu, J. 136
Zero set of  functions 302
Zero set of an analytic function 10
Zero set, structure of 299
Zygmund, A. 123
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