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


Kurbanov V.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, cilt.41, ss.347-364, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 41 Konu: 3
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1556/sscmath.41.2004.3.7
  • Dergi Adı: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
  • Sayfa Sayıları: ss.347-364

Özet

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.