Half line Titchmarsh–Weyl m functions of vector-valued discrete Schrödinger operators
ANNALS OF FUNCTIONAL ANALYSIS(2021)
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.
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Key words
Vector-valued discrete Schrodinger operators, Titchmarsh-Weyl m functions, Transfer matrices, Herglotz functions
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