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Half line Titchmarsh–Weyl m functions of vector-valued discrete Schrödinger operators

Half line Titchmarsh–Weyl m functions of vector-valued discrete Schrödinger operators We show that the half-line m functions associated with the vector-valued discrete Schrödinger operators are the elements in the Siegel upper half space. We introduce a metric on the space of m functions associated to these operators. Then, we show that the action of transfer matrices on these m functions is distance decreasing. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Functional Analysis Springer Journals

Half line Titchmarsh–Weyl m functions of vector-valued discrete Schrödinger operators

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Publisher
Springer Journals
Copyright
Copyright © Tusi Mathematical Research Group (TMRG) 2021
ISSN
2639-7390
eISSN
2008-8752
DOI
10.1007/s43034-021-00140-x
Publisher site
See Article on Publisher Site

Abstract

We show that the half-line m functions associated with the vector-valued discrete Schrödinger operators are the elements in the Siegel upper half space. We introduce a metric on the space of m functions associated to these operators. Then, we show that the action of transfer matrices on these m functions is distance decreasing.

Journal

Annals of Functional AnalysisSpringer Journals

Published: Aug 9, 2021

Keywords: Vector-valued discrete Schrödinger operators; Titchmarsh–Weyl m functions; Transfer matrices; Herglotz functions; 39A70; 47A05

References