Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail: Keywords: ordinary differential operator; eigenvalues; eigenfunctions and associated functions; root functions; expansion in biorthogonal series; Riesz basis property; completeness of the system eigenfunction and associated functions; pencil of ordinary differential operators; multiple completeness of the system of eigenfunctions and associated functions; Green's function; regular boundary conditions; nonregular boundary conditions.
Subject:
An asympthotic of the fundamental system of solutions of the differential equation generated by ordinary linear differential expression of the $n$th order with a spectral parameter and nonsmooth coefficient at $n-1$st derivative was built. For the ordinary differential operator, generated by this differential expression and regular two-point boundary conditions, theorems of equiconvergence of the expansions of an arbitrary function in biorthogonal series with respect to the eigen- and associated functions of this operator and in the ordinary trigonometric Fourier series were proved. Estimates of the rate of equiconvergence were given. Conditions of completeness and Riesz basisness of the system of eigen- and associated functions of this operator in the space of summable with square functions were found.
Main publications:
V. S. Rykhlov. Asymptotical formulas for solutions of linear differential systems of the first order // Results in Mathematics, v. 36, no. 3–4, 1999, p. 342–353.
G. Freiling, V. Rykhlov. Pointwise convergence of eigenfunctions for a general class of regular eigenvalue problems // Methods of Functional Analysis and Topology, 1997, v. 3, p. 27–45.
V. S. Rykhlov. Equiconvergence rate in terms of general moduli of continuity for differential operators // Results in Mathematics, v. 29, no. 1, 1996, p. 153–168.
