Full paper in PDF format:
$%B. X. Fejzullahu, Divergent Cesàro Means of Jacobi-Sobolev Expansions, Rev. Mat. Complut. 21 (2008), no. 2, 427–433.%$

Divergent Cesàro Means
of Jacobi-Sobolev Expansions
Bujar Xh. FEJZULLAHU
Faculty of Mathematics and Sciences
University of Prishtina
Nëna Terezë 5
10000 Prishtinë — Kosovo
bujarfej@uni-pr.edu
Received: February 2, 2007
Accepted: November 22, 2007

ABSTRACT

Let μ be the Jacobi measure supported on the interval [-1,1] . Let introduce the Sobolev-type inner product

∫ 1 ′ ′ ⟨f,g⟩= -1f(x)g(x)dμ(x)+ Mf (1)g(1)+ Nf (1)g (1),

where M, N ≥ 0 . In this paper we prove that, for certain indices δ , there are functions whose Cesàro means of order δ in the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product are divergent almost everywhere on [- 1,1] .

Key words: Jacobi-Sobolev type polynomials, Fourier expansion, Cesàro mean.
2000 Mathematics Subject Classification: 42C05, 42C10.