Equiconvergence property for spectral expansions related to perturbations of the operator - u''(-x) with initial data
Keyword(s):
Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution: -u''(-x) and -u''(-x) + q(x)u(x) with the initial data u(-1) = 0, u'(-1) = 0 is obtained. Starting with the spectral analysis of the unperturbed operator, the estimates of the Green?s functions are established and then applied via the contour integrating approach to the spectral expansions. As a corollary, it is proved that the root functions of the perturbed operator form the basis in L2(-1,1) for any complex-valued coefficient q(x) ? L2(-1,1).
2021 ◽
2016 ◽
Vol 52
(12)
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pp. 1563-1574
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2016 ◽
Vol 16
(2)
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pp. 165-174
2020 ◽
Vol 12
(3)
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pp. 15-21
1980 ◽
Vol 14
(1)
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pp. 11-15
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