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Full-Text Articles in Analysis
Titchmarsh–Weyl Theory For Vector-Valued Discrete Schrödinger Operators, Keshav R. Acharya
Titchmarsh–Weyl Theory For Vector-Valued Discrete Schrödinger Operators, Keshav R. Acharya
Publications
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.
Action Of Complex Symplectic Matrices On The Siegel Upper Half Space, Keshav R. Acharya, Matt Mcbride
Action Of Complex Symplectic Matrices On The Siegel Upper Half Space, Keshav R. Acharya, Matt Mcbride
Publications
The Siegel upper half space, Sn, the space of complex symmetric matrices, Z with positive definite imaginary part, is the generalization of the complex upper half plane in higher dimensions. In this paper, we study a generalization of linear fractional transformations, ΦS, where S is a complex symplectic matrix, on the Siegel upper half space. We partially classify the complex symplectic matrices for which ΦS(Z) is well defined. We also consider Sn and Sn as metric spaces and discuss distance properties of the map ΦS from Sn to Sn and Sn respectively.