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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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Abel's lemma 101 Acyclic cohomology 266 Adjoint of the 186 Adjoint of the 190 Adjoint of the 1 77 Admissible approach region 356 Admissible convergence for holomorphic functions 354 Admissible limits for holomorphic functions 360 Admissible limits re-examined 362 Admissible regions 353 Admissible set for the Kobayashi/Royden metric 440 Affinity function 250 259 Aleksandrov, A.B. 12 383 397 Alexander, H. 439 Alexander, H., Rudin's generalization 480 Alexander, H., theorem 480 Almost analytic extensions 424 Analytic continuation 14 242 318 Analytic convexity 241 Analytic disc 136 Analytic polyhedron 160 166 483 484 Analytic sheaf 293 Analytic space 131 Analytic type 466 467 Analytic, closed 136 Andreotti, A. 9 175 292 Approximation of a holomorphic function 14 419 Approximation theory 236 Artinian ring 275 Ascoli — Arzela theorem 45 Atlas 493 Automorphism group of 431 Automorphism group of a domain 429 Automorphism group of the ball 70 480 Automorphisms of bounded circular domains 430 Bagemihl — Seidel theorem 349 373 Baire category theorem 108 Baire class 33 Banach — Alaoglu theorem 322 Barbell domain 242 Barker, S.R. 358 Barrett, D. 462 Basener, R. 141 170 Basin of attraction 477 Beatrous, F. 233 Bedford, E. 97 98 141 161 479 Behnke — Stein theorem 158 Bell, S. 59 70 455 462 Bell, S. lemma 457 Berg, C. 73 Bergman and Hardy spaces 307 Bergman and Kobayashi/Royden metrics, incomparability of 491 Bergman distance 56 Bergman kernel 49 Bergman kernel for the ball 62 Bergman kernel, calculation of 76 Bergman kernel, extremal property of 57 Bergman kernel, transformation under a mapping 55 Bergman kernel, uniqueness of 51 Bergman metric 56 434 Bergman metric for the ball 63 Bergman metric, definiteness of 79 Bergman metric, dominates the Caratheodory metric 490 Bergman metric, geodesic of 65 Bergman metric, isometry of 56 Bergman projection 52 Bergman space 50 Bergman space, basis for 79 Bergman — Bell projection formula 459 Bergman, S. 49 Besicovitch's theorem 103 beta function 61 Betti numbers 136 Biholomorphic inequivalence of the ball and the polydisc 65 Biholomorphic mapping 9 55 429 Biholomorphic of finite type domains 475 Bishop, E. 314 Blank, B. 441 Blaschke condition 328 379 Blaschke factorization 327 Blaschke product 12 381 Boas, H. 58 59 Bochner — Martinelli form 291 Bochner — Martinelli formula 22 Bochner — Martinelli kernel 30 Bochner, extension phenomenon 210 Bochner, S. 49 99 Bogoliubov, N. 161 Bonneau, P. 227 Bonneson, T. 117 Borel's theorem 103 256 469 Boundary values, specifying 396 Bounded linear operator 176 Bounded mean oscillation, function of 374 377 Boutet de Monvel, L. 59 68 70 234 Branched covering 300 Braun — Karp — Upmeier linearization theorem 430 Braun, R. 430 Bremerman, H. 8 99 Bungart, L. 69 227 Burbea, J. 490 Burns, D. 9 430 435 453 454 Calderon theorem 349 Calderon, A.P. 348 Campbell — Baker — Hausdorff formula 311 Canonical construction 495 Canonical distance 436 Canonical distance, minimality of 441 Canonical factorization 12 329 382 Canonical kernels vs. constructible kernels 70 Canonical metric 434 435 Canonical metric isometries 487 Canonical metrics on the polydisc 483 Canonical solution to the a problem 198 Canonical theorem 371 Canonical volume form 446 Canonical vs. Henkin solution for the a problem 406 Caratheodory, Cartan — Kaup — Wu theorem 444 Carleson, L. 297 Cartan formula 232 314 508 Cartan theorem 429 Cartan theorem A 293 295 Cartan theorem B 293 295 Cartan, H. 254 429 Catlin sub ellipticity theorem 475 Catlin, D. 384 464 470 Cauchy estimates 104 Cauchy formula for the polydisc 31 Cauchy integral formula 20 24 Cauchy — Fantappie formula 77 226 407 Cauchy — Riemann equation 15 Cauchy — Riemann equation with non-smooth solution 194 Cauchy — Riemann equation without closed range 212 Cauchy — Riemann equation, inhomogeneous 15 25 27 28 34 Cauchy, A. 117 Cayley transform, generalized 112 Cegrell, U. 98 Chain homotopy 31 260 Chain rule 76 Chang, D.C. 470 Chebycheff's inequality 324 Chern class 285 Chern map 285 Chern — Moser invariants 453 Chern, S.S. 10 60 Chirka, E. 362 365 Christ, F.M. 470 475 Cima, J. 307 362 365 376 488 Circled set 104 Circular domain 104 Closed operator 177 Closure of adjoint operator 1 78 Closure of range lemma 1 79 Coboundary 257 Coboundary operator 257 290 Cochains 256 Cocycles 257 Coherent analytic sheaf 294 Cohomologous 259 Cohomology group 290 Cohomology of slices 286 Combinatorial topology 243 Common refinement 262 Commutator 466 Compactly divergent subsequence 439 Comparability of canonical metrics and Euclidean metric in the interior 487 Comparison domains, method of 331 Complete circular domain 104 Complete Reinhardt domain 104 Completeness of the canonical metrics 482 483 488 Complex affine space 94 Complex analytic dynamics 476 Complex foliation 485 Complex line 94 Complex manifold 295 Complex normal 465 Complex normal curve 372 Complex projective space, cohomology of 287 Complex structure tensor 124 Complex tangent space 125 355 Complexification 103 Condition r 455 462 475 Cone 161 324 Conjugate holomorphic vector field 466 Connecting morphism 265 Constant sheaf 256 Continuously differentiable 3 Convex function 81 114 Convex set, geometrically 11 7 Convex, strongly 120 Convexifiability 136 Convexity 9 117 Convexity with respect to a family of functions 129 Convexity, affine sphere characterization 131 Convexity, analytic 120 Convexity, and domains of holomorphy 156 Convexity, hyperplane characterization 164 Convexity, strict 130 Convexity, strong, 130 Convolution of forms 30 Convolution of two functions 26 Coordinate chart 493 Coordinate pair 493 Cordoba, A. 357 Corona problem 297 298 Corona theorem 297 Cotangent vector 504 Counting zeros of a holomorphic function 308 Cousin problem 12 Cousin problem, first 247 Cousin problem, first, for 247 Cousin problem, first, solution 247 Cousin problem, first, with bounds 418 Cousin problem, second 247 Cousin problem, second, application 253 Cousin problem, second, for meromorphic functions 283 Cousin problem, second, non-solvability of 250 Cousin problem, second, solution 249 CoverIng by geometrically simple subdomains 341 Covering lemma 323 Cumenge, A. 421 Currents 30 D'Angelo, decomposition of a defining function 474 D'Angelo, J. 423 464 470 488 Dales, H.G. 241 Davie, A.M. 233 de Rham theorem, holomorphic 273 274 de Rham theorem, real 272 Defining function 3 71 11 Defining function, pullback of 172 Demailly, J.P. 9 Diaz, R. 307 Diederich, K. 168 421 462 Differential form 3 19 504 Differentials 2 Direct limit 259 Dirichlet problem 43 Distance decreasing properties of canonical metrics 438 Distance function 142 Distance function, smoothness of 164 distribution 27 201 Distribution function 349 Divergence 37 Divisor 11 282 Dixon, P. 170 479 Dolbeault complex 268 Dolbeault isomorphisms 287 Dolbeault theorem 268 Domain 3 Domain algebra, prescribing boundary values in 401 Domain of boundedness for a power series 104 Domain of convergence for a power series 13 104 Domain of convergence, characterization of 106 Domain of holomorphy 6 Domain of holomorphy, characterization of 131 153 Douglas, R. 233 Edge-of-the-wedge theorem 161 162 166 Ehren preiss, L. 9 33 Eilenberg — MacLane spaces 292 Envelope of holomorphy 240 318 Epstein, B. 73 Equivalence of geometric and analytic type 469 Essential point 153 Essential point, locally 157 Esterle, J. 170 479 Estimates for the a operator 403 Estimates for the a operator on ellipsoids 421 Estimates for the a operator, basic 192 Estimates for the a operator, optimal 418 Estimates for the a operator, sharp 464 Estimates for the a operator, uniform 411 Euclidean Hartogs figure, generalized 292 Euclidean space 1 Exhaustion function 191 Existence theorem for the a operator 194 Extension of an analytic function 14 213 Exterior derivative 507 Exterior differential operator 20 Exterior product 500 Faa de Bruno 113 459 Factoring holomorphic functions 12 310 Faran, J. 488 Farkas, H. 441 Fatou — Bieberbach domain 170 476 Fatou, P. 476 Federbush, P. 97 Federer, H. 495 Fefferman analytic type 468 Fefferman geometric type 468 Fefferman lemma 1 71 Fefferman theorem 210 377 462 Fefferman type 470 472 Fefferman type 2, genericity of 491 Fefferman, C. 10 59 60 68 70 351 354 357 376 441 443 453 470 Fenchel, W. 117 Fermat, P. 117 Finite 1-type 472 Finsler metric 434 Fisher, S. 441 Foliation 310 312 433 486
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