Dependence rate of equiconvergence on the module of continuity of potential of the Sturm-Liouville operator

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Kurbanov V.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, vol.41, no.3, pp.347-364, 2004 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 41 Issue: 3
• Publication Date: 2004
• Doi Number: 10.1556/sscmath.41.2004.3.7
• Journal Name: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.347-364
• Van Yüzüncü Yıl University Affiliated: No

Abstract

In this paper we consider the problem of local uniform equiconvergence with trigonometric series of orthogonal expansions in a system of eigenfunctions of the Sturm-Liouville operator with real potential q(x) is an element of L-1 (0, 1), for the function f (x) from the classes W-1(1) (0, 1) and W-r(1) (0, 1) (r greater than or equal to 1), f (0) = f (1) = 0. Rate of equiconvergence on every compact subset of (0, 1) is established. Rate of equiconvergence depends on the module of continuity of potential.