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• W2949530058 abstract "We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schrodinger operators on $[a,infty)$, $ainmathbb{R}$, with a regular finite end point $a$ and the case of Schrodinger operators on the real line with locally integrable potentials, which naturally lead to Herglotz functions and $2times 2$ matrix-valued Herglotz functions representing the associated Weyl-Titchmarsh coefficients. Second, we contrast this with the case of self-adjoint half-line Schrodinger operators on $(a,infty)$ with a potential strongly singular at the end point $a$. We focus on situations where the potential is so singular that the associated maximally defined Schrodinger operator is self-adjoint (equivalently, the associated minimally defined Schrodinger operator is essentially self-adjoint) and hence no boundary condition is required at the finite end point $a$. For this case we show that the Weyl-Titchmarsh coefficient in this strongly singular context still determines the associated spectral function, but ceases to posses the Herglotz property. However, as will be shown, Herglotz function techniques continue to play a decisive role in the spectral theory for strongly singular Schrodinger operators." @default.
• W2949530058 created "2019-06-27" @default.
• W2949530058 creator A5007268689 @default.
• W2949530058 creator A5053434924 @default.
• W2949530058 date "2005-05-06" @default.
• W2949530058 modified "2023-09-27" @default.
• W2949530058 title "On Spectral Theory for Schrodinger Operators with Strongly Singular Potentials" @default.
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• W2949530058 hasPublicationYear "2005" @default.
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