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Titlebook: An Advanced Complex Analysis Problem Book; Topological Vector S Daniel Alpay Textbook 2015 Springer International Publishing Switzerland 20

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de Branges–Rovnyak SpacesThe de Branges–Rovnyak spaces are reproducing kernel spaces which appear in various fields, from operator theory to interpolation theory, stochastic processes and system theory. In this chapter we merely outline some of their elementary properties.
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Bergman SpacesAs already said, Bergman spaces seem to form the first example of reproducing kernel Hilbert spaces of analytic functions. In this chapter we discuss the case of the disk and the polyanalytic cases. More involved cases, such as the annulus and the ellipse, are only mentioned .. We urge the reader to look at these cases.
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Das Wachstum der lebendigen Masseinner product spaces. A distinguished class of Hilbert spaces, namely reproducing kernel Hilbert spaces, is studied at a later stage in Chapter .. These various notions play an important role in the third part of the book, dedicated to spaces of analytic functions and their operators.
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Durch wieviel Lebensalter gehen wir?,eorem, and more generally, of its vector–valued version, namely the Beurling–Lax theorem. They also play a key role in the theory of linear systems. The fractional Hardy spaces play an important role in the theory of self–similar systems.
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Hardy Spaceseorem, and more generally, of its vector–valued version, namely the Beurling–Lax theorem. They also play a key role in the theory of linear systems. The fractional Hardy spaces play an important role in the theory of self–similar systems.
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