Spectral Multipliers for Schrödinger Operators: 1

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Abstract

We prove a sharp Mihlin-Hörmander multiplier theorem for Schrödinger operators H on R n . The method, which allows us to deal with general potentials, improves Hebisch’s method relying on heat kernel estimates for positive potentials [22, 12]. Our result applies to, in particular, the negative Pöschl-Teller potential V ( x )=− v ( v +1)sech 2 x , v N , for which H has a resonance at zero. Moreover, a modified heat kernel approach is used to obtain the multiplier result for unbounded electric and magnetic potentials arising in a relativistic quantum-mechanical background. Thus it helps the understanding of quantum scattering for wave and Schrödinger systems.
Original languageAmerican English
JournalInterdisciplinary Mathematics Institute Preprint Series
Volume2007
StatePublished - 2007

Keywords

  • Littlewood-Paley theory
  • Schrödinger operator
  • Spectral multiplier

DC Disciplines

  • Mathematics

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