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Titlebook: An Introduction to Operators on the Hardy-Hilbert Space; Rubén A. Martínez-Avenda?o,Peter Rosenthal Textbook 2007 Springer-Verlag New York

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期刊全稱An Introduction to Operators on the Hardy-Hilbert Space
影響因子2023Rubén A. Martínez-Avenda?o,Peter Rosenthal
視頻videohttp://file.papertrans.cn/156/155410/155410.mp4
發(fā)行地址More elementary than the competition.Contains clear and beautiful proofs.Has been class-tested a number of times.Includes supplementary material:
學科分類Graduate Texts in Mathematics
圖書封面Titlebook: An Introduction to Operators on the Hardy-Hilbert Space;  Rubén A. Martínez-Avenda?o,Peter Rosenthal Textbook 2007 Springer-Verlag New York
影響因子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
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Die Bewertung der Hochofeneinsatzstoffe,We introduce the unilateral shift, one of the most interesting operators. The study of the invariant subspaces of this operator leads naturally to a factorization of functions in ..
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Introduction,In this chapter, we introduce the main definitions and establish some fundamental properties of the Hardy-Hilbert space that we use throughout this book. We also describe various results from functional analysis that are required, including some properties of the spectrum and of invariant subspaces.
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The Unilateral Shift and Factorization of Functions,We introduce the unilateral shift, one of the most interesting operators. The study of the invariant subspaces of this operator leads naturally to a factorization of functions in ..
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