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Dineen S. — Complex Analysis of Infinite Dimensional Spaces
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.


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(BB)_{n}$-property      32 37 40 78 101 442
$(BB)_{\infty}$-property      32 242 275 286 331
$c_{p}$ space      79
$\aleph_{0}$-barrelled space      464
$\beta$-topology      31 187
$\epsilon$-product      77 102
$\Lambda$ space      452
$\lambda$-nuclear space      240
$\mathcal{A}$-domain of holomorphy      337 388
$\mathcal{A}$-envelope of holomorphy      337 388
$\mathcal{A}$-extension      337
$\mathcal{C}^{*}$ algebra      51 79 417
$\mathcal{DFC}$ space      164 382 395 458 463 483
$\mathcal{DFM}$ space      27 37 68 78 98 132 155 159 172 179 186 214 222 236 354 357 376 402 458 463
$\mathcal{DFN}$ space      71 97 100 174 291 294 314 357 390 407 410 443 453
$\mathcal{DFS}$ space      78 137 154 175 214 234 314 386 390 421 439 449 458 472
$\mathcal{G}$-holomorphic function      74 144 229 439 460
$\mathcal{S}$-absolute decomposition      190 197 199 204 214 215 225 240 245 271 279 295 436 445 465 469 483
$\mathcal{s}$-nuclear space      240
$\mathcal{S}$-Schauder decomposition      314
$\mathcal{S}$-stable collection      195
$\Omega$-space      443
$\overline{\partial}$ operator      366 395
$\overline{\partial}$ problem      76 174 241 319 323 366
$\varepsilon$-tensor product      77 102 470
($\underline{DN}$)-property      410 443
($\widetilde{\Omega}$)-property      241 389 422 472
(BB)-property      33 35 38 71 78 175 316 453
(DN)-property      241 265 302 313 319 389 411 470 472 474
A-nuclear space      206 227 241 290 310 466
Abel's theorem      232
Absolute basis      28 201 205 209 228 241 287 290 291 302 307 308 310 321 439 454 457 462 466 472
Absolute decomposition      189 245 259
Absolutely summing series      458
Absorbing set      27
Adjoint      5 70 424 451
Algebra, $\mathcal{C}^{*}$      51 79 417
Algebra, commutative      416
Algebra, Frechet      241 340 370
Algebra, locally m-convex      223 237 340 370 386 424 457
Algebra, Stein      241
Algebra, structure      416
Algebra, symmetric      77 457
Algebraic basis      146 247 402 447 460
Algebraic dual      2
Almost uniform copy      54
Ambiguity, point of      326
Ambiguity, set of      326
Analytic continuation      168 231 234 340 349 359 389 392
Analytic functional      166 287 292 316 450 462
Analytic set      441 482
Approximable polynomial      85 427
Approximation number      320
Approximation property      89 93 94 112 124 129 131 134 135 228 254 271 274 298 313 314 376 382 388 396 427 430 436 441 455.
Approximation property, $\lambda$      89
Approximation property, bounded      89 270 271 286 300 314 318 323 354 360 373 379 380 383 389 395 407 409 424 437 439 469 471 474 478
Approximation property, compact      134 459 466
Approximation property, metric      80 90 134 239 467
Approximation property, strict      90 94 102 296
Arens regular      415 417 424
Aron — Berner extension      55 58 79 80 125 134 283 412 415 426 428 431 434 440 443 451 456 480
Ascoli's theorem      183
Asplund holomorphic mapping      481
Asplund space      108
Associated barrelled topology      192 199
Associated bornological topology      25 32 171 192 240 452
Associated infrabarrelled topology      199 240
Associated topology      227 240 316
Auerbach basis      461
Averaging techniques      450
B-continuous function      448
Baire category theorem      153 374 449
Baire first class, function of      154 448
Baire space      221 448 452
Banach disc      194
Banach — Dieudonne theorem      448 465
Banach — Mackey theorem      194
Banach — Mazur distance      45 320
Banach — Steinhaus theorem      449
Barrelled space      27 71 97 170 172 188 192 209 222 224 271 289 354 384
Basic sequence      118 123 251 273 309
Basis constant      251 255
Basis, absolute      28 201 205 209 228 241 287 290 291 302 307 308 310 321 439 454 457 462 466 472
Basis, algebraic      146 247 402 447 460
Basis, Auerbach      461
Basis, boundedly complete      214 465
Basis, countable algebraic      402 441
Basis, equicontinuous      304
Basis, generalized      219 460
Basis, Hamel      146 247 447
Basis, monomial      205 208 249 253 304
Basis, monotone      124 251
Basis, Schauder      42 139 189 201 205 246 249 252 254 271 287 311 318 360 366 395 459 465 471 478
Basis, shrinking      124 247 252 310 314 315
Basis, unconditional      68 121 124 176 249 287 290 304 309 311 387 460 471 476
Baxtle integral      455
Bernoulli random variable      8
Bernstein's inequality      51
Bessaga — Pelczyriski selection principle      118 272
Bidual      55 79 125 129 136 412 419 425 435 444 458 482
Bidual, holomorphic      434
Bidual, natural      58
Biholomorphic mapping      50
Bilinear form      5 75 134 307 321 416 440
Bilinear mapping      2 32 443
Binomial theorem      12
Bipolar      58
Blaschke product      478
Bohr inequality      321
Borel measure      104 132
Borel transform      93 104 287 295 312 317
Bornological DF space      32 40 98 222 234 295 330 463
Bornological space      25 35 38 71 97 170 172 183 256 277 290
Bounded approximation property      89 270 271 286 300 314 318 323 354 360 373 379 380 383 389 395 407 409 424 437 439 469 471 474 478
Bounded nuclear type      295 472
Bounded open topology      22 77
Bounded set      18 21 31 33
Bounded sets, lifting of      131 456
Boundedly complete basis      214 465
Boundedly complete decomposition      214
Bounding holomorphic mapping      481
Bounding set      141 157 166 172 234 298 309 311 373 380 400 403 412 419 443 461 462 468 471 479
Boyd index      139
Calculus of variations      230
Canonical mapping      70 80 97 126 425
Carleman inequality      10
Cartan — Thullen theorem      167 323 357 358 476
Cauchy inequalities      50 149 230 264 298 344 399 401 418 423
Cauchy integral formula      145 230
Cauchy — Riemann equations      144 232
Chart      333
Commutative algebra      416
Compact approximation property      134 459 466
Compact holomorphic mapping      138 481
Compact linear mapping      83 88 90 450
Compact non-polar set      405 409
Compact open topology      21 77 166 336 393
Compact polydisc      202 204 288 292
Compact polynomial      68 84 88 118 137
Complemented subspace      35 38 69 90 174 176 237 270 300 318 420 470 473
Completion, holomorphic      389 399 400 442 478
Completion, pseudo-convex      443
Complex norm      69 450
Conditionally compact set      234
Continuum Hypothesis      447
Contractive projection      50 55
Control function      404
Control set      404 443
Convolution      434 444
Convolution operator      135 297 441 445
Coordinate functional      145 147
CoType      56 61 320
Countable algebraic basis      402 441
Countable inductive limit      25 27 277
Countable neighbourhood property      281 317
Countable open cover      169 173 208 341 370
Countably barrelled space      225 464
Decomposition      196
Decomposition, absolute      189 245 259
Decomposition, basic      188
Decomposition, boundedly complete      214
Decomposition, equi-Schauder      188 252
Decomposition, finite dimensional      241 249 252 255 259 267 271 310 314 459 470 471
Decomposition, monotone      189 256 259
Decomposition, S-absolute      190 197 199 204 214 215 225 240 245 271 279 295 436 445 465 469 483
Decomposition, Schauder      188 224 239 245 250 257 262
Decomposition, shrinking      196 255 273 311 465
Decomposition, T.S.-complete      213
Decomposition, unconditional      189 259 274
Decomposition, unordered      189
Density condition      40 58 101 286
Desirable norm      450
Determining set      180 225 312 439 461 465
DF space      26 35 78 98 175 222 277 295 309 357 462
Diagonal mapping      4 55 206
Diagonal operator      84
Dirac delta function      29 72 167 184 431
Dirichlet series      231 322
Dispersed set      133
Distinguished space      27 40 387 390 441 452 482
Domain of Existence      354 358 373 376 381 385 399 404 405 439 475 477
Domain of holomorphy      76 233 337 354 385 386 389 394 475
Domain, holomorphically convex      168. 186 324 340 353 355 358 373 389 394 403
Domain, holomorphically separated      346 354 381
Domain, metrically holomorphically convex      478
Domain, polynomially convex      235 316 384 386 388 394
Domain, pseudo-convex      168 233 319 324 340 353 356 366 376 381 383 387 392 403 404 439
Domain, PSH($\Omega$)-convex      355
Domain, PSH-convex      353 395
Domain, Reinhardt      387 476
Domain, Riemann      237 323 333 343 391 398 430 434 444
Dual nuclear space      94 136 240 301 318
Dual space      2 31 274
Dual, algebraic      2
Dual, fourth      426
Dual, inductive      23 30 183 216
Dual, strong      18 22 207
Dunford — Pettis property      114 117 138 256 314 451 480
Dunford — Pettis Property, polynomial      451 472
Dunford — Pettis Property, reciprocal      141
Dvoretzky Spherical Sections Theorem      46 56 61 320
Envelope of bounded holomorphy      428
Envelope of holomorphy      168 236 316 337 338 384 385 388 396 398 463 477
Envelope of linearity      434
Equi-Schauder decomposition      188 252
Equicontinuous basis      304
Equicontinuous set      15 18 27 30 183 288 296
Euler's identity      76
Even monomials      268
Expected value      8 321
Exponential law      473
Exponential type      298 318 462
Extendible polynomial      439 480
Extension      411
Extension, Aron — Berner      55 58 79 80 125 134 283 412 415 426 428 431 434 440 443 451 456 480
Extension, holomorphic      337 350 385 388 393 400 419 442
Extremal constant      41 79
Extremal polynomial      45 48 450
Extreme point      70 128 451
Factorization lemma      16 58 77 101 161 482
Finite dimensional decomposition      241 249 252 255 259 267 271 310 314 459 470 471
Finite intersection property      327
Finite open topology      144 161 287 296 447
Finitely generated ideal      483
Finitely represented      46
First non-trivial superproperty      56
Frechet algebra      241 340 370
Frechet differentiable function      229
Frechet holomorphic function      74 152
Frechet nuclear space      174 241 257 265 286 291 294 302 312 318 390 407 408 444 462 463 468 474
Frechet space      16 27 101
Frechet space, T-decomposable      317
Frechet — Montel space      27 37 41 130 212 236 247 257 275 286 309 316 331 391 469
Frechet — Schwartz space      286 310 316 323 332 384 386 389 467 469 474 476
Fully nuclear space      74 97 136 202 231 241 247 287 293 294 296 300 309 316 386 405
Function of nuclear type      295
Function, $\mathcal{G}$-holomorphic      74 144 229 439 460
Function, control      404
Function, Dirac delta      29 72 167 184 431
Function, exponential type      298 318 462
Function, Frechet differentiable      229
Function, Frechet holomorphic      74 152
Function, generalized Rademacher      63 80 449
Function, Grothendieck integrable      108
Function, holomorphic      74 144 152
Function, holomorphic of bounded type      112 135 164 286 295 412 421 431 441 445 469 473 476
Function, hypoanalytic      159 204 221 294
Function, locally weakly uniformly continuous      255
Function, lower semi-continuous      335
Function, Lusin measurable      108
Function, multiplicative      415 418
Function, Pietsch integrable      108
Function, plurisubharmonic      352 403 438 447 468
Function, Rademacher      116 139
Function, real analytic      450
Function, separately holomorphic      144 154 165 221 233 461
Function, Silva holomorphic      136 467
Function, subharmonic      352
Function, uniformly bounded type      165 228 422
Function, universally measurable      108 460
Function, upper semi-continuous      385
Function, weakly holomorphic      160 173
Functional calculus      421
Functional, analytic      166 287 292 316 450 462
Functional, coordinate      145 147
Functional, multiplicative      168 340 343 379 381 415 424 427
Fundamental neighbourhood system      25 28 39 58 203 211 260 281 294 295 308 344
Fundamental sequence      122
Fundamental system of bounded sets      25 26 330
Fundamental system of compact sets      28 203 260 308 330 358 390 408
Gantmacher's Theorem      451
Gateaux derivative      75
Gateaux differentiable function      149 448
Gateaux holomorphic extension      477
Gateaux holomorphic function      74 144 229 439 460
Gaussian measure      319 442 483
gDF space      282 311 317 462
Generalized basis      219 460
Generalized Rademacher functions      63 80 449
Goldstine's Theorem      104 126 482
Grothendieck integrable function      108
Grothendieck property      141
Grothendieck space      131
Grothendieck — Pietsch criterion      201 205 208 257 266 309 332 422 468
Grothendieck's $\varepsilon-\pi$ conjecture      320
Grothendieck's Completeness Theorem      145 185
Hadamard three circles theorem      404
Hamel basis      146 247 447
Hardy — Littlewood inequality      308
Hartogs' theorem      144 154 233 461
Hemi-compact space      163
Hereditary Lindeloef space      228
Hermitian form      5 73
Hilbert space      52 56 61 68 71 72 79 130 395 420 452
Holomorphic bidual      434
Holomorphic completion      389 399 400 442 478
Holomorphic extension      337 350 385 388 393 400 419
Holomorphic factorization      162
Holomorphic function      74 144 152
Holomorphic function of bounded type      112 135 164 286 295 412 421 431 441 445 469 473 476
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