Dineen S. — Complex Analysis of Infinite Dimensional Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Dineen S. — Complex Analysis of Infinite Dimensional Spaces

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Название: Complex Analysis of Infinite Dimensional Spaces

Автор: Dineen S.

Аннотация:

This book considers basic questions connected with, and arising from, the locally convex space structures that may be placed on the space of holomorphic functions over a locally convex space. The first three chapters introduce the basic properties of polynomials and holomorphic functions over locally convex spaces. These are followed by two chapters concentrating on relationships between the compact open topology, the ported or Nachbin topology and the topology generated by the countable open covers. The concluding chapter examines the interplay between the various concepts introduced earlier as being intrinsic to infinite dimensional holomorphy. The comprehensive notes, historical background, exercises, appendix and bibliography make this book an invaluable reference whilst the presentation and synthesis of ideas from different areas will appeal to mathematicians from many different backgrounds.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 543

Добавлена в каталог: 17.11.2013

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Предметный указатель

Silva holomorphic function      136 467
Solid hull      202
Solid set      202
Space, $c_{p}$       79
Space, $\aleph_{0}$ -barrelled      464
Space, $\Lambda$       452
Space, $\lambda$ -nuclear      240
Space, $\mathcal{DFC}$       164 382 458 463 483
Space, $\mathcal{DFM}$       27 37 68 78 98 132 155 159 172 179 186 214 222 236 354 357 376 402 458 463
Space, $\mathcal{DFN}$       71 97 100 174 291 294 314 357 390 407 410 443 453
Space, $\mathcal{DFS}$       78 137 154 175 214 234 314 386 390 421 439 449 458 472
Space, $\omega$       443
Space, A-nuclear      206 227 241 290 310 466
Space, Asplund      108
Space, Baire      221 448 452
Space, barrelled      27 71 97 170 172 188 192 209 222 224 271 289 354 384
Space, bornological      25 35 38 71 97 170 172 183 256 277 290
Space, bornological DF      32 40 98 222 234 295 330 463
Space, countably barrelled      225 464
Space, DF      26 35 78 98 175 222 277 309 357 462
Space, distinguished      27 40 387 390 441 452 482
Space, dual      2 31 74
Space, dual nuclear      94 136 240 301 318
Space, Frechet      16 27 101
Space, Frechet nuclear      174 241 257 265 286 291 294 302 312 318 390 407 408 444 462 463 468 474
Space, Frechet — Montel      27 37 41 130 212 236 247 257 275 286 309 316 331 391 469
Space, Frechet — Schwartz      286 310 316 323 332 384 386 389 467 469 474 476
Space, fully nuclear      74 97 136 202 231 241 247 287 293 294 296 300 309 316 386 405
Space, gDF      282 311 317 462
Space, Grothendieck      131
Space, hemi-compact      163
Space, hereditary Lindeloef      228
Space, Hilbert      52 56 61 68 71 72 79 130 395 420 452
Space, holomorphically barrelled      235 462 465
Space, holomorphically infrabarrelled      235
Space, holomorphically Mackey      235 465
Space, infrabarrelled      97 222 290 435 465
Space, injective      117
Space, k      132 282 323 330 331 458
Space, Koethe sequence      257 311 331
Space, LB      239
Space, Lindeloef      71 130 163 372 379 395 402 463
Space, m-regular      443
Space, Mackey      227 466
Space, Montel      27 100 258 308 312 459
Space, nuclear      175 205 207 240 308 318 421 478
Space, Orlicz      139
Space, power series      228 266 267 409 467
Space, primary      470
Space, prime      41
Space, Q-reflexive      125 129 140 435 445 455
Space, quasi-barrelled      97
Space, quasi-complete      22 215 344
Space, quasi-normable      131 217 226 239 242 317 390 456 463 464
Space, quasi-reflexive      124
Space, reflexive      27 113 254 270 275 442
Space, reflexive A-nuclear      207
Space, reflexive nuclear      270
Space, regular      415
Space, s-nuclear      240
Space, Schwartz      218 242 258 310 438 463
Space, second countable      372
Space, semi-Montel      22 219 281
Space, semi-reflexive      27 97 226 271
Space, sequence      201 257 311 331
Space, stable      37 440
Space, strong nuclear      241
Space, superinductive      154
Space, superreflexive      61
Space, symmetrically regular      424 426 428 430 440 444
Space, totally reflexive      227 466
Space, Tsirelson      121 134 138 256 272 438 442 466 473
Space, Tsirelson — James      124 129 256 437
Space, twisted      237
Space, ultrabornological      170 233 277 466
Space, uniformly convex      229
Space, universal      469
Space, weakly compactly generated      234 470
Space, weighted      445
Spectral theory      229
Spectrum      324 424 444
Spectrum, $\tau_{0}$       343
Spectrum, bounded      340
Splitting condition      244 409
Spreading model      60 122 133 139
Square order      247 252 254 271 311 313 315
Stable space      37 440
Stein algebra      241
Stirling's formula      45 51 297 304 432
Stone — Cech compactification      133 259
Strict approximation property      90 94 102 296
Strict inductive limit      28 130 137 223 311 464 469 471
Strict Mackey convergence criterion      137 464
Strictly polar set      403
Strong dual      18 22 207
Strong localization property      283 285 317 474
Strong nuclear space      241
Strong topology      21 31 39
Subharmonic function      352
Super (P)      56

Superinductive limit      234
Superinductive space      154
Superproperty      56 80
Superreflexive space      61
Surjective limit      28 163 236 387 449 455 462 478
Symmetric algebra      77 457
Symmetric mapping      6 416
Symmetric matrix      5 307
Symmetric measure      459
Symmetric tensor      7 35 77 182 313 457
Symmetrically regular space      424 426 428 430 440 444
Symmetrization operator      6 29 414
Szegoe's inequality      79
T-morphism      336
T.S. complete      213 242 271
Taylor series expansion      13 74 149 231
Tensor      3 7 35 77 182 313 457
Tensor product      3 134 238
Tensor product, injective      102 267
Tensor product, n-fold      3
Tensor product, projective      29 32 125
Tietze extension theorem      462
Topology of pointwise convergence      67 182 214 378 448
Topology of uniform convergence      18 21
Topology, $\beta$       31 187
Topology, $\pi$       33 103
Topology, $\pi_{0}$       92 95 295
Topology, $\pi_{b}$       92
Topology, $\pi_{\delta}$       295
Topology, $\pi_{\omega}$       92—94 295
Topology, $\tau_{0}$       21 77 166 336 393
Topology, $\tau_{b}$       22 200 241 317
Topology, $\tau_{\delta}$       169 170 199 237 262 301 336 341 384 393 401
Topology, $\tau_{\omega}$       23 78 169 237 270 278 336 383 437 463 475
Topology, $\tau_{\pi}$       390
Topology, $\varepsilon$       103
Topology, associated      240 316
Topology, associated barrelled      192 199
Topology, associated bornological      25 32 171 192 240 452
Topology, associated infrabarrelled      199 240
Topology, associated ultrabornological      227
Topology, bounded open      22 77
Topology, compact open      21 77 166 336 393
Topology, finite open      144 161 287 296 447
Topology, inductive      23 78
Topology, injective      102
Topology, localized      282
Topology, Mackey      99
Topology, Nachbin      23 78 169 463
Topology, ported      23 78 169 463
Topology, projective      19 33 41 103
Topology, sheaf      390
Topology, strong      21 31 39
Topology, weak polynomial      140
Total derivative      73
Totally reflexive space      227 466
Trace      64
Transfinite induction      193 240 465
Translation operator      441
TRANSPOSE      5 59 341 348 424
Tsirelson space      121 134 138 256 272 438 442 466 473
Tsirelson — James space      124 129 256 437
Twisted quojection      162 471
Twisted subspace      237
TYPE      320
Ultrabornological space      170 223 277 466
Ultrafilter      55 60 122 427
Ultrapower      55 57 60 80 122
Ultraproduct      55
Unconditional basis      68 121 124 176 249 287 290 304 309 311 387 460 471 476
Unconditional decomposition      189 259 274
Unconditionality constant      123
Uniform continuity      85—87
Uniform Frechet algebra      241
Uniform holomorphy      164 223 237 241
Uniformly bounded type      165 228 422
Uniformly convex space      229
Uniformly polar set      438
Universal space      469
Universally measurable function      108 460
Unordered basis      189
Upper p-estimate      121 139
Upper semi-continuous      385
Very strongly convergent net      224
Very strongly convergent sequence      177 214 224 312 388 464 476
Weak holomorphic convergence      311 470
Weak holomorphy      461
Weak*-continuity      60
weakly compact mapping      70 415 440 481
Weakly compact set      416 466
Weakly compactly generated space      234 470
Weakly continuous mapping      427 444
Weakly continuous polynomial      65 70
Weakly holomorphic function      160 173
Weakly null sequence      114 118 124 139 459
Weakly sequentially continuous polynomial      113 116 133 137 141 274
Weakly summable series      130 458
Weight      201 207
Weighted space      445
X-Koethe space      460
Zero-one law      483

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