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On the Domain of a Magnetic Schrödinger Operator with Complex Electric Potential

In: Analysis and Operator Theory

Author

Listed:
  • Bernard Helffer

    (CNRS and Université de Nantes)

  • Jean Nourrigat

    (LMR EA 4535 and FR CNRS 3399, Université de Reims Champagne-Ardenne, Moulin de la Housse)

Abstract

The aim of this paper is to review and compare the spectral properties of the Schrödinger operators $$-\varDelta + U$$ - Δ + U ( $$U\ge 0$$ U ≥ 0 ) and $$-\varDelta + i V$$ - Δ + i V in $$L^2(\mathbb R^d)$$ L 2 ( R d ) for $$C^\infty $$ C ∞ real potentials U or V with polynomial behavior. The case with magnetic field will be also considered. We present the existing criteria for essential self-adjointness, maximal accretivity, compactness of the resolvent, and maximal inequalities. Motivated by recent works with X. Pan, Y. Almog, and D. Grebenkov, we actually improve the known results in the case with purely imaginary potential.

Suggested Citation

  • Bernard Helffer & Jean Nourrigat, 2019. "On the Domain of a Magnetic Schrödinger Operator with Complex Electric Potential," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Valentin A. Zagrebnov (ed.), Analysis and Operator Theory, pages 149-165, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-12661-2_8
    DOI: 10.1007/978-3-030-12661-2_8
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