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January  2019, 18(1): 397-424. doi: 10.3934/cpaa.2019020

Spectral expansion series with parenthesis for the nonself-adjoint periodic differential operators

Received  January 2018 Revised  April 2018 Published  August 2018

In this paper we construct the spectral expansion for the differential operator generated in $L_{2}(-∞, ∞)$ by ordinary differential expression of arbitrary order with periodic complex-valued coefficients by introducing new concepts as essential spectral singularities and singular quasimomenta and using the series with parenthesis. Moreover, we find a criteria for which the spectral expansion coincides with the Gelfand expansion for the self-adjoint case.

Citation: Oktay Veliev. Spectral expansion series with parenthesis for the nonself-adjoint periodic differential operators. Communications on Pure & Applied Analysis, 2019, 18 (1) : 397-424. doi: 10.3934/cpaa.2019020
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