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

✍ Scribed by G. Rozenblum; M. Solomyak

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 223 KB
Volume: 208
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.10.041

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✦ Synopsis

We study a family of differential operators L in two variables, depending on the coupling parameter 0 that appears only in the boundary conditions. Our main concern is the spectral properties of L , which turn out to be quite different for < 1 and for > 1. In particular, L has a unique self-adjoint realization for < 1 and many such realizations for > 1. In the more difficult case > 1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved.

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