Lμ → Lν equiconvergence of spectral decompositions for a Dirac system with Lκ potential
- Authors: Sadovnichaya I.V.1
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Affiliations:
- Faculty of Computational Mathematics and Cybernetics
- Issue: Vol 93, No 2 (2016)
- Pages: 223-226
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223627
- DOI: https://doi.org/10.1134/S1064562416020307
- ID: 223627
Cite item
Abstract
It is proved that if P ∈ Lκ[0, π], κ ∈ (1, ∞], then the expansions of any function f ∈ Lμ[0, π], μ ∈ [1, ∞], in the generalized eigenfunctions of the perturbed and unperturbed operators are equiconvergent in the norm of the space Lν[0, π], provided that ν ∈ [1, ∞] satisfies the inequality \(\frac{1}{\kappa } + \frac{1}{\mu } - \frac{1}{\nu } \leqslant 1\), except in the case where κ = ν = ∞ and μ = 1.
About the authors
I. V. Sadovnichaya
Faculty of Computational Mathematics and Cybernetics
Author for correspondence.
Email: ivsad@yandex.ru
Russian Federation, Moscow, 119991