The Il’in Spectral Method for Determination of the Properties of the Basis Property and the Uniform Convergence of Biorthogonal Expansions on a Finite Interval

DOI10.18500/1816-9791-2019-19-1-34-58zbMath1430.46007OpenAlexW2927071109MaRDI QIDQ5230131

I. S. Lomov

Publication date: 20 August 2019

Published in: Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/isu788

zbMATH Keywords

second-order differential operatorunconditional basisspectral method

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Cites Work

• Integral representations of irregular root functions of loaded second-order differential operators
• Riesz bases formed by root functions of a functional-differential equation with a reflection operator
• Conditions for the absolute and uniform convergence of the biorthogonal series corresponding to a differential operator
• The basis problem of the eigenfunctions of ordinary differential operators with integral boundary conditions
• The development of general differential and general differential-boundary systems
• Estimates of root functions of the adjoint of a second-order differential operator with integral boundary conditions
• Uniform convergence of biorthogonal series for the Schrödinger operator with multipoint boundary conditions
• Properties of spectral expansions corresponding to non-self-adjoint differential operators.
• Resolvent approach in the Fourier method
• Estimates of Speed of Convergence and Equiconvergence of Spectral Decomposition of Ordinary Differential Operators
• EQUICONVERGENCE THEOREMS FOR INTEGRODIFFERENTIAL AND INTEGRAL OPERATORS
• The Bessel inequality and the basis property of root functions of a second-order singular differential operator
• Boundary value problems with discontinuity conditions in an interior point of the interval
• Equiconvergence of expansions over eigenfunctions of finite-dimensional perturbations of an integration operator
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