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February 21, 2026

On Estimates of the Rate of Equiconvergence of SpectralExpansions for the Dirac System with a Summable Potential

Key Points

The central aim is to estimate the rate of equiconvergence of spectral expansions for the Dirac system with summable potentials.
Analyzed spectral expansions of the Dirac system on a finite interval.
Assumed boundary conditions to be Birkhoff-regular.
Provided estimates for square summable functions and Sobolev spaces.
Qualified estimates of equiconvergence rates were determined for square-summable potentials.
Distinct estimates for functions in Sobolev spaces were presented.

Abstract

This article is devoted to estimating the rate of equiconvergence of spectral expansions for the Dirac system on a finite interval. The potential of the operator is assumed to be summable, and the boundary conditions are Birkhoff-regular. Results are obtained for the case where the expanded function f is square summable, and qualified estimates of the equiconvergence rate are separately provided for the case of a square-summable potential and a function f from the scale of Sobolev spaces.

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