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.
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Acknowledgements
The author sincerely thanks the anonymous referee for going over this manuscripts in detail, and providing valuable remarks and suggestions which improved the paper. This work was partially supported by the Office of Sponsored Research at Embry-Riddle Aeronautical University, Florida (Grant No. ERAU 13256).
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Acharya, K.R. Titchmarsh–Weyl theory for vector-valued discrete Schrödinger operators. Anal.Math.Phys. 9, 1831–1847 (2019). https://doi.org/10.1007/s13324-018-0277-x
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DOI: https://doi.org/10.1007/s13324-018-0277-x