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

2005/11/15 by Fritz Gesztesy, Gesztesy, Fritz, Vadim Tkachenko +1
Mathematics · Physics and Astronomy · #34B30 #34L05 #34L40 #47A10 #47B40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34B30 #msc:34L05 #msc:34L40 #msc:47A10 #msc:47B40

paper · pdf · doi:10.48550/arxiv.math/0511370

5 pages

arxiv created 2005/11/15 · openalex publication_date 2005/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H=-d²/dx²+V in L²(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.

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