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Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions

Djakov, Plamen Borissov and Mityagin, Boris (2012) Equiconvergence of spectral decompositions of 1D Dirac operators with regular boundary conditions. Journal of Approximation Theory, 164 (7). pp. 879-927. ISSN 0021-9045

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Official URL: http://dx.doi.org/10.1016/j.jat.2012.03.013

Abstract

One dimensional Dirac operators L-bc(nu) y = i ((1)(0) -(0)(1)) dy/dx +nu(x)y. y = ((y2) (y1)). x is an element of [0, pi], considered with L-2-potentials nu(x) = ((0)(P(x)) (P(x))(0)) and subject to regular boundary conditions (bc), have discrete spectrum. For strictly regular be, the spectrum of the free operator L-bc(0) is simple while the spectrum of L-bc(nu) is eventually simple, and the corresponding normalized root function systems are Riesz bases. For expansions of functions of bounded variation about these Riesz bases, we prove the uniform equiconvergence property and point-wise convergence on the closed interval [0, pi]. Analogous results are obtained for regular but not strictly regular bc.

Item Type:Article
Uncontrolled Keywords:Dirac operators; Spectral decompositions; Riesz bases; Equiconvergence
Subjects:Q Science > QA Mathematics
ID Code:19183
Deposited By:Plamen Borissov Djakov
Deposited On:18 Jul 2012 14:39
Last Modified:20 Jul 2012 11:26

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