When is a non-self-adjoint Hill operator a spectral operator of scalar type?

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We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H=-d^2/dx^2+V in L^2(R) to be a spectral operator of scalar type. The conditions demonstrate the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V.
5 pages

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Spectral Theory, Mathematical Physics, 34B30; 47B40; 47A10; 34L05; 34L40

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http://salesiana.dossiersoluciones.com/handle/123456789/104926

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511370
 http://arxiv.org/abs/math/0511370

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arXiv