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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 2, 2002, pp. 351–370
DOI: 10.4171/ZAA/1082

Published online: 2002-06-30

Pseudodifferential Operators with Analytic Symbols and Estimates for Eigenfunctions of Schrödinger Operators

Vladimir S. Rabinovich[1]

(1) Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico

We study the behavior of eigenfunctions of the Schrödinger operator $–\Delta + \nu$ with potential having power, exponential or super-exponential growth at infinity and discontinuities on manifolds in $\mathbb R^n$. We use a connection between the domain of analyticity of the main symbol $(|\xi|^2 + \nu (x))^{–1}$ of the parametrix $–\Delta + \nu$ at infinity or near singularities of $\nu$ and the behavior of eigenfunctions at infinity or near singularities of potentials. Our approach is based on a general calculus of pseudodifferential operators with analytic symbols.

Keywords: Pseudodifferential operators, analytic symbols, Schrödinger operators

Rabinovich Vladimir S.: Pseudodifferential Operators with Analytic Symbols and Estimates for Eigenfunctions of Schrödinger Operators. Z. Anal. Anwend. 21 (2002), 351-370. doi: 10.4171/ZAA/1082