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Krantz S.G. — Function Theory of Several Complex Variables
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Название: Function Theory of Several Complex VariablesАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2nd editionГод издания: 2000Количество страниц: 564Добавлена в каталог: 01.06.2008Операции: Положить на полку |
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Folland, G.B. 175 Forelli's theorem 96 Fornass imbedding theorem 135 222 386 Fornass — Krantz theorem 222 Fornass, J. 9 13 141 168 222 421 462 476 Forstneric, F. 488 Forward light cone 161 Fourier multiplier 205 Fourier transform 203 Frankel, S. 479 Freeman, M. 241 314 Fridman, B. 10 454 Frobenius integrability theorem 311 312 Function, 493 Function, 493 Function, holomorphic on a manifold 493 Function, real analytic on a manifold 493 Fundamental solution 27 29 30 Fundamental solution for the Laplacian 37 114 203 Gain in regularity 464 Gamelin, T.W. 297 Gamma function of Euler 60 Garnett, J. 297 351 Gauss's lemma 275 Geometric type 464 Gilbarg, S. 143 Gleason problem 13 422 Gleason, A. 69 227 Graded union 504 Graham theorem 442 Graham, C.R. 112 Graham, I. 76 374 441 443 Grauert, H. 9 25 70 216 292 314 407 411 419 Green function 42 43 Green function for the ball 46 Green theorem 35 Green, M. 476 Greene — Krantz theorem 454 Greene, R.E. 9 10 58 60 221 435 446 453 479 Greiner, P. 367 422 Guan, P. 470 Guilleman, V. 161 Hahn, K.T. 490 Hakim — Sibony approximation scheme 167 386 Hakim, M. 383 Hardy class 302 321 339 Hardy class, boundary limits for 321 Hardy class, real variable theory of 351 376 Hardy — Littlewood lemma 411 Hardy — Littlewood maximal function 324 Hardy — Littlewood theorem 373 Hardy, G.H. 374 Harmonic function 35 Harmonic function, maximum principle for 40 41 Harmonic function, mean value property for 39 Harmonic function, square of 70 Harmonic majorant 338 341 Harnack inequalities 72 Harnack principle 72 Hartogs domain 232 Hartogs extension phenomenon 8 33 75 106 Hartogs figure, generalized 292 Hartogs figure, simple 291 Hartogs functions 93 99 Hartogs lemma 32 91 Hartogs phenomenon 79 Hartogs pseudoconvexity 143 Hartogs triangle 169 Hartogs, F. 8 Harvey, R. 73 241 Hatziafratis, T. 227 Hausdorff measure 495 Hausdorff topology on domains 59 Hefer's lemma 224 244 Heisenberg group 112 Henkin integral formula 225 Henkin integral solution in 408 Henkin solution operator for the a problem 406 Henkin, G.M. 11 25 70 216 227 302 379 419 432 489 Henon map 476 Hermitian inner product 354 Hessian complex 126 Hessian real 120 Hilbert space 50 176 Hilbert space with reproducing kernel 66 Hille, E. 362 Hironaka, H. 300 Hoermander, L. 9 175 Holomorphic convexity 240 Holomorphic curve 471 Holomorphic extension 318 Holomorphic function 4 31 32 Holomorphic function, constructing 17 25 Holomorphic function, fake 200 Holomorphic function, maximum principle for 40 Holomorphic function, removable set for 300 Holomorphic inverse 55 Holomorphic mapping with a fixed point 429 Holomorphic p-form 271 Holomorphic support function 138 Holomorphic vector field 466 Holomorphy, domain of 151 Homogeneity argument 122 Homogeneous coordinates 287 Hopf Lemma 49 73 461 489 Huckleberry, A. 432 Hull with respect to a family of functions 152 Hurwitz theorem 76 310 Hyper bolicity 483 Hypoadmissible convergence 363 Hypoadmissible curve 377 Hypoellipticity, failure of 421 Ideal 275 Ideal, maximal 275 Ideal, sheaf 296 Imbedding 432 Implicit function theorem 3 Implicit function theorem, holomorphic 54 Increasing sums 1 79 Indeterminate point 282 Inequivalence of ball and polydisc 239 432 453 Inequivalence of Kobayashi metric and Bergman metric 482 Inequivalence of weakly and strongly pseudo convex domains 433 Infinitesimal form of the canonical metrics on the ball 480 Inner function 381 Inner function, closure of 396 Inner function, existence of 395 Inner function, problem 382 Inner function, singular 382 Inner product for vector fields 505 Integral divisor 282 Integral domain 275 Integral manifold 311 Integration on a manifold 506 Interior estimates for the 424 Interior multiplication 36 Interior product 501 Interpolation of operators 358 Invariance of finite type 491 Irreducible ring element 275 Isometries of the canonical metrics 438 Isometries, determined by first order behavior 444 Isotropic balls 352 356 Isotropy group 432 Iwasawa decomposition 113 Jacobian 53 Jacobian, complex 53 Jacobian, real 53 Jacobowitz, H. 423 Jensen inequality 328 Jewell, N. 233 John — Nirenberg theorem 376 Jones, P.W. 197 297 Jordan canonical form 444 Josefson, B. 98 Julia, G. 476 Karp, W. 430 Kashiwara, M. 161 Kawai, T. 161 Kelvin inversion 45 Kerzman — Rosay theorem 482 Kerzman, N. 13 59 70 168 216 331 407 411 419 423 Kim, K.T. 479 Kiselman, C. 462 Klembeck, P. 60 Klimek, M. 98 Kobayashi metric 365 371 Kobayashi metric, one disc 485 Kobayashi, S. 79 Kobayashi/Eisenman volume form 446 Kobayashi/Royden distance, integrated 482 Kobayashi/Royden distance, maximality of 440 Kobayashi/Royden length of a curve 437 Kobayashi/Royden metric 434 437 Kobayashi/Royden metric, isometries 487 Kodama, A. 479 Kohn global regularity theorem for the 207 426 Kohn solution to the a equation 195 Kohn — Nirenberg domain 167 Kohn — Nirenberg example 140 Kohn, J.J. 9 129 175 314 422 427 463 470 Kontinuitatssatz 144 Koppelman, W. 78 Koranyi, A. 354 KOREVAAR, J. 164 Koszul complex 239 Kra, I. 441 Krantz estimates on the Kobayashi metric 486 Krantz, S.G. 9 10 58 60 99 103 143 175 221 233 307 351 362 365—367 370 374 376 377 421 430 435 441 446 453 470 479 488 Kugelsatz 8 291 Laplacian 35 Laplacian, self-adjointness of 204 Latter, R. 351 Lefschetz, S. 244 476 Lehto, O. 362 Lelong, P. 378 Lempert theorem 442 Lempert theorem applications 443 Lempert, L. 10 347 454 462 Leray form 21 Leray theorem 263 Leray, J. 254 Levi form 126 128 190 433 Levi form, coordinate free definition 232 Levi form, rank of 312 Levi polynomial 216 Levi problem 8 29 131 215 Levi problem for complete circular domains 158 Levi problem for tube domains 160 Levi problem, consequences of 158 Levi problem, solution of 215 Levi pseudoconvex 128 Levi pseudoconvex, strongly 128 Lewy — Pincuk reflection principle 207 Lewy, H. 423 Lieb, I. 25 70 216 407 411 419 Lindeloef principle 362 376 Lindeloef principle for hypoadmissible convergence 364 Lindeloef principle, failure for admissible convergence 363 Liouville theorem 114 Lipschitz estimate for the 415 416 Lipschitz estimate for the 416 Lipschitz space 365 411 Lipschitz space, nonisotropic 366 Littlewood, J.E. 374 Local coordinates for studying the Henkin solution 409 Local Parametrization Theorem 471 Local ring 275 Local solvability 426 Localization of singularities 227 Locally finitely generated sheaf 293 Locally regularly presented manifold 295 Logarithm convexity 105 Logarithm of a set 105 Lojaciewicz exact cohomology sequence 265 268 Lojaciewicz theorem 491 Lojaciewicz, S. 103 279 Long 170 Low, E. 12 383 395 Lower semicontinuous function 81 Lu conjecture 58 Lu Qi-Keng 490 Ma, D. 10 351 377 MAIN GOAL 183 Manifold 493 Manifold, 493 Manifold, $C^{\infty} 493 Manifold, diffeomorphism of 493 Manifold, mapping of 493 Manifold, product of 494 Manifold, real analytic 493 Manifold, smooth 493 Manifold, union of 494 MAP 429 Mapping 429 Mapping problem 59 Marcinkiewicz interpolation theorem 371 Marshall's theorem 395 Martin, W. 99 Maximal function, characterization of Hardy spaces 351 Maximal function, comparison of 351 McNeal, J. 141 475 Mergelyan theorem 14 Minkowski functional 124 Minkowski, H. 117 Mittag — Leffler theorem 11 75 254 Model domain 438 Modified 188 Monge-Ampere equation 98 Morrey, C.B. 9 175 Moser, J. 10 60 Multi vector 504 Multi-covector field 504 Multi-index notation 3 Multiplicity of a holomorphic function 471 Nagel — Rudin theorem 372 Nagel, A. 13 354 470 475 Narasimhan lemma 134 171 Narasimhan, R. 9 314 Nebenhiille 142 Nevanlinna class 301 302 379 Nirenberg — Webster — Yang proof of Fefferman's theorem 489 Nirenberg, L. 129 Noell, A. 384 Noetherian ring 275 Non-continuable holomorphic function 7 Non-locally solvable operator 422 Non-smooth biholomorphic mapping 485 489 491 Non-uniqueness of Kobayashi/Royden extremals 489 Non-vanishing Jacobian of a biholomorphism 486 Nonisotropic balls 352 356 Nontangential approach region 324 Nontangential boundary limits for holomorphic functions 326 330 349 Nontangential boundedness and nontangential limits 348 Norguet, F. 8 Normal family 439 482 Normal function 376 Normal vector 118 Normalized complex tangential curve 366 Normalized holomorphic function 276
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