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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 work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. While due homage is paid to the more traditional algebraic theory (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2000

Количество страниц: 564

Добавлена в каталог: 01.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Normally convergent sequence      439
Oka coherence theorem      295
Oka extension theorem      286
Oka map      237
Oka principle      249
Oka, K.      8
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 existence and uniqueness theorem      310
Picard 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 lemma      95 270
Poincare metric      484
Poincare Problem, strong      284
Poincare — Bergman distance      436
Poincare — Bergman metric for the disc      63
Poincare, H.      10 453
Poisson integral for the ball      48
Poisson integral formula      43
Poisson kernel for the ball      46
Poisson kernel, lower bound for      332 334
Poisson kernel, uniqueness of      49
Poisson kernel, upper bound for      337
Poisson — Szegoe kernel      67
Poisson — Szegoe kernel and solution of a Dirichlet problem      111
Poisson — Szegoe kernel for the ball      69
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 $C^j$ 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 mapping theorem      10 58
Riemann metric      435
Riemann spread domains      316
Riesz decomposition      378
Riesz representation theorem      50
Riesz — Fischer theorem      52
Right inverse for a      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 lemma      489 490
Royden, H.      443
Rudin, W.      11 161 170 301 302 307 370 373 382—384 479
Runge approximation property      229
Runge domain      239 481
Runge property      229 231
Runge theorem      14
Ryll — Wojtaszczyk polynomials      383
Sard's theorem      149
Schur's lemma      72
Schwartz distribution      203
Schwartz space      203
Schwarz 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 cohomology      256 257
Sheaf of germs of $C^{\infty}$ 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 projection      254
Sheaf, fine      258
Sheaf, global sections of      262
Sheaf, section of      254
Sheaf, stalk of      254
Sheng, G.      354
Shirkov, D.      161
Shnider, S.      9 453 454
Sibony counterexample to the corona theorem      372
Sibony, N.      13 136 141 194 297 383 423
Siegel domain      112 160 1
Siegel, C.L.      276
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 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 imbedding theorem      196
Sobolev imbedding theorem on domains      204
Sobolev space      196 197 202
Spencer, D.C.      175
Stability result for the a problem      415
Stein lemma      339
Stein manifolds      314
Stein manifolds, imbedding of      314
Stein theorem      367
Stein, E.M.      37 70 164 348 351 354 358 367 373 376 407 422 464 470 475
Stein, K.      9 432
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 kernel      66
Szegoe kernel for the ball      69
Szegoe, G.      49
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 theorem      77
Taylor, B.A.      98
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      1 76
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 type of a curve      472
Variety type vs. regular type      473
Variety, analytic      471
Variety, irreducible      471
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 pseudo convex domains      158
Webster, S.      488
Wedge product      500
Weierstrass division theorem      278
Weierstrass polynomial      276
Weierstrass preparation theorem      276
Weierstrass theorem      11
Weight functions      185
Weighted $L^2$ space      182 183
Weighted Sobolev spaces      1 75
Weil domains      159
Weil, A.      270
Weiss, G.      37 164
Wells, R.      9 435 453 454 465
Wermer example      482
Wermer, J.      13
Weyl's lemma      42 200
Whitney decomposition of an open set      111
Whitney, H.      495
Widman, K.O.      348
Wiegerinck, J.      58 96 110 115 164 421
Wiener covering lemma      345
Wolff, T.      297
Wong lemma      447
Wong — Rosay theorem      447
Wong, B.      479
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 $H^p$ functions      302
Zero set of an analytic function      10
Zero set, structure of      299
Zygmund, A.      123
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