JournalszaaVol. 21, No. 2pp. 351–370

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

  • Vladimir S. Rabinovich

    Escuelo Superior de Mat y Fis del IPN, México, D.f., Mexico
Pseudodifferential Operators with Analytic Symbols and Estimates for Eigenfunctions of Schrödinger Operators cover
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Abstract

We study the behavior of eigenfunctions of the Schrödinger operator Δ+ν–\Delta + \nu with potential having power, exponential or super-exponential growth at infinity and discontinuities on manifolds in Rn\mathbb R^n. We use a connection between the domain of analyticity of the main symbol (ξ2+ν(x))1(|\xi|^2 + \nu (x))^{–1} of the parametrix Δ+ν–\Delta + \nu at infinity or near singularities of ν\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.

Cite this article

Vladimir S. Rabinovich, Pseudodifferential Operators with Analytic Symbols and Estimates for Eigenfunctions of Schrödinger Operators. Z. Anal. Anwend. 21 (2002), no. 2, pp. 351–370

DOI 10.4171/ZAA/1082