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Dispersive Properties of Schrödinger Operators in the Absence of a Resonance at Zero Energy in 3D

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Evolution Equations of Hyperbolic and Schrödinger Type

Part of the book series: Progress in Mathematics ((PM,volume 301))

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Abstract

In this paper we study spectral properties associated to the Schrödinger operator − Δ −Wwith potential W that is an exponentially decaying C 1 function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of resonances for the NLS.

Mathematics Subject Classification. Primary 35B34; Secondary 35L05.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Sciences, Pisa University, Largo Pontecorvo 5, I-56127, Pisa, Italy

    Vladimir Georgiev & Mirko Tarulli

Authors
  1. Vladimir Georgiev
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  2. Mirko Tarulli
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Corresponding author

Correspondence to Vladimir Georgiev .

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Editors and Affiliations

  1. , Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom

    Michael Ruzhansky

  2. , Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

    Mitsuru Sugimoto

  3. , Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany

    Jens Wirth

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Georgiev, V., Tarulli, M. (2012). Dispersive Properties of Schrödinger Operators in the Absence of a Resonance at Zero Energy in 3D. In: Ruzhansky, M., Sugimoto, M., Wirth, J. (eds) Evolution Equations of Hyperbolic and Schrödinger Type. Progress in Mathematics, vol 301. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0454-7_7

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