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Titlebook: Operator Theory; Daniel Alpay Reference work 2015 Springer Basel 2015 Schur analysis.de Branges spaces.indefinite inner product spaces.inf

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发表于 2025-3-21 16:16:32 | 显示全部楼层 |阅读模式
书目名称Operator Theory
编辑Daniel Alpay
视频video
概述Embraces the long history, diversity and wide range of topics relating to operator theory.Explores notions such as positivity and reproducing kernel through interconnected sections.Describes multiple
图书封面Titlebook: Operator Theory;  Daniel Alpay Reference work 2015 Springer Basel 2015 Schur analysis.de Branges spaces.indefinite inner product spaces.inf
描述A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
出版日期Reference work 2015
关键词Schur analysis; de Branges spaces; indefinite inner product spaces; infinite dimensional analysis; nonco
版次1
doihttps://doi.org/10.1007/978-3-0348-0667-1
isbn_ebook978-3-0348-0667-1
copyrightSpringer Basel 2015
The information of publication is updating

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Locally Definitizable Operators: The Local Structure of the Spectrumype and spectral points of type .. and type ..: It turns out that all spectral subspaces corresponding to sufficiently small neighborhoods of spectral points of positive/negative type are Hilbert or anti-Hilbert spaces and spectral subspaces corresponding to spectral points of type .. or type .. are
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Reproducing Kernels in Coherent States, Wavelets, and Quantization show its applications to the theory of coherent states, coherent state and Berezin-Toeplitz quantization, and to the related theory of the continuous wavelet transform. The aim is to demonstrate the unifying mathematical aspect, given by the reproducing kernel, of these different theories.
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Geometric Perspectives on Reproducing Kernelst derivatives, and curvatures. The correspondence from kernels to connections is achieved through a pullback operation from the tautological universal bundle, using a suitable classifying morphism for the given kernel. The theory is illustrated by several examples including classical kernels in func
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Multi-valued Operators/Linear Relations Between Kreĭn Spacesn. More precisely, the basic properties of these indefinite inner product spaces, which are generalizations of Hilbert spaces, are described, where the similarities to and differences compared with Hilbert spaces are emphasized. Secondly, the basic properties of multi-valued operators, which are gen
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