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Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators

Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators We develop the Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators. We show that the Weyl m functions associated with these operators are matrix valued Herglotz functions that map complex upper half plane to the Siegel upper half space. We discuss about the Weyl disk and Weyl circle corresponding to these operators by defining these functions on a bounded interval. We also discuss the geometric properties of Weyl disk and find the center and radius of the Weyl disk explicitly in terms of matrices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators

Analysis and Mathematical Physics , Volume 9 (4) – Dec 17, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Nature Switzerland AG
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-018-0277-x
Publisher site
See Article on Publisher Site

Abstract

We develop the Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators. We show that the Weyl m functions associated with these operators are matrix valued Herglotz functions that map complex upper half plane to the Siegel upper half space. We discuss about the Weyl disk and Weyl circle corresponding to these operators by defining these functions on a bounded interval. We also discuss the geometric properties of Weyl disk and find the center and radius of the Weyl disk explicitly in terms of matrices.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 17, 2018

References