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On Spectral Properties of Schrödinger-Type Operator with Complex Potential

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Recent Developments in Operator Theory and Its Applications

Part of the book series: Operator Theory Advances and Applications ((OT,volume 87))

Abstract

Let T be the operator (-Δ)m + q(x) on L 2(ℝn). Assume that the ”principal” part of ℜq(x) is positive, ”regular” and tends to infinity as|x| → ∞, and ℑq is relatively form-bounded with respect to (-Δ)m + ℜq(x) with relative bound zero (therefore T has purely discrete spectrum). In the framework of the general perturbation approach, we study the spectral asymptotics and the Riesz basisness for the generalized eigenfunctions of T.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Bar - Ilan University, Ramat - Gan, 52900, Israel

    Edward Grinshpun

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  1. Edward Grinshpun
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

  2. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1NA, Canada

    P. Lancaster

  3. Department of Applied Mathematics and Institute of Industrial Mathematical Sciences, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada

    P. N. Shivakumar

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© 1996 Birkhäuser Verlag Basel/Switzerland

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Grinshpun, E. (1996). On Spectral Properties of Schrödinger-Type Operator with Complex Potential. In: Gohberg, I., Lancaster, P., Shivakumar, P.N. (eds) Recent Developments in Operator Theory and Its Applications. Operator Theory Advances and Applications, vol 87. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9035-9_7

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  • DOI: https://doi.org/10.1007/978-3-0348-9035-9_7

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9878-2

  • Online ISBN: 978-3-0348-9035-9

  • eBook Packages: Springer Book Archive

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