Research of equiconvergence for differential operator with involution in case of summated potential

Author(s):  E.Yu. Romanova, candidate of Sciences, Voronezh State University, Voronezh, Russia, vsu.romanova@gmail.com

Issue:  Volume 50, № 4

Rubric:  Mathematics

Annotation:  The paper deals with the differential operator L with involution, defined by a differential ex * pression ( ) ( ) ( ) ( ), [0, ], ([0, ], ), 1 l y = yў x -Q x y w - x xО w QОL w C and boundary conditions y(0) = y(w) . The method of similar operators is used to analyze the spectral properties of the operator. The asymptotic of spectrum and the equiconvergence of spectral decomposition are obtained

Keywords:  spectrum of operator, differential operator with involution, summated potential, similar operators method, asymptotic of spectrum, spectral decomposition, equiconvergence of spectral decomposition

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