On a family of differential operators with the coupling parameter in the boundary condition

  • Authors:

  • G. Rozenblum;M. Solomyak

  • Affiliations:

  • Department of Mathematics, Chalmers University of Technology and The University of Gothenburg, S-412 96, Gothenburg, Sweden;Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2007

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Abstract

We study a family of differential operators Lα intwo variables, depending on the coupling parameter α≥0that appears only in the boundary conditions. Our main concern isthe spectral properties of Lα, which turn out tobe quite different for αa1. Inparticular, Lα has a unique self-adjointrealization for α1. In the more difficult case α1 an analysisof non-elliptic pseudodifferential operators in dimension one isinvolved.