On a class of Model Hilbert Spaces

Fritz Gesztesy; Rudi Weikard; Maxim Zinchenko

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arXiv · 1111.0645

On a class of Model Hilbert Spaces

Fritz Gesztesy·Rudi Weikard·Maxim Zinchenko

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Abstract

We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure. In particular, we show that several alternative approaches to such a construction in the literature are equivalent. These spaces are of fundamental importance in the context of perturbation theory of self-adjoint extensions of symmetric operators, and the spectral theory of ordinary differential operators with operator-valued coefficients.

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BibTeX RIS

Fritz Gesztesy, Rudi Weikard, Maxim Zinchenko. 2011-11-02. On a class of Model Hilbert Spaces. https://arxiv.org/abs/1111.0645

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