Inverse spectral theory for random Jacobi matrices (Q1826216)
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scientific article; zbMATH DE number 4122993
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse spectral theory for random Jacobi matrices |
scientific article; zbMATH DE number 4122993 |
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Inverse spectral theory for random Jacobi matrices (English)
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1987
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For stationary Jacobi matrices the \(w\)-functions are defined and studied. It turns out that these \(w\)-functions are special Herglotz functions. Starting with such a Herglotz function a stationary Jacobi matrix is constructed having it as \(w\)-function, i.e. necessary and sufficient conditions are given for a Herglotz function to be a \(w\)-function of a random stationary Jacobi matrix. The theory is explained selfconsistently and up to some detail.
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random Schrödinger operator
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stationary Jacobi matrices
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Herglotz functions
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