Divergent Cesàro Means of Jacobi-Sobolev Expansions
نویسنده
چکیده
Let μ be the Jacobi measure supported on the interval [−1, 1]. Let introduce the Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f(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].
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