| 期刊全称 | An Introduction to Operators on the Hardy-Hilbert Space | | 影响因子2023 | Rubén A. Martínez-Avendaño,Peter Rosenthal | | 视频video | | | 发行地址 | More elementary than the competition.Contains clear and beautiful proofs.Has been class-tested a number of times.Includes supplementary material: | | 学科分类 | Graduate Texts in Mathematics | | 图书封面 |  | | 影响因子 | The great mathematician G. H. Hardy told us that “Beauty is the ?rst test: there is no permanent place in the world for ugly mathematics” (see [24, p. 85]). It is clear why Hardy loved complex analysis: it is a very beautiful partofclassicalmathematics. ThetheoryofHilbertspacesandofoperatorson themisalmostasclassicalandisperhapsasbeautifulascomplexanalysis. The studyoftheHardy–Hilbertspace(aHilbertspacewhoseelementsareanalytic functions), and of operators on that space, combines these two subjects. The interplay produces a number of extraordinarily elegant results. For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. 1. 21 below) and Cauchy integral (Theorem 1. 1. 19) formulas. The fundamental theorem about zeros of fu- tions in the Hardy–Hilbert space (Corollary 2. 4. 10) is the central ingredient of a beautiful proof that every continuous function on [0,1] can be uniformly approximated by polynomials with prime exponents (Corollary 2. 5. 3). The Hardy–Hilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2. 2. 12). Conversely, pr- erties of the unilat | | Pindex | Textbook 2007 |
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发表于 2025-3-21 18:34:14
