Research Article A Cohen-Type Inequality for Jacobi-Sobolev Expansions
نویسندگان
چکیده
Let μ be the Jacobi measure supported on the interval [−1, 1]. Let us introduce the Sobolev-type inner product 〈 f ,g〉 = ∫ 1 −1 f (x)g(x)dμ(x) + M f (1)g(1) + N f ′(1)g′(1), where M,N ≥ 0. In this paper we prove a Cohen-type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product. We follow Dreseler and Soardi (1982) and Markett (1983) papers, where such inequalities were proved for classical orthogonal expansions.
منابع مشابه
A Cohen Type Inequality for Fourier Expansions of Orthogonal Polynomials with a Non-discrete Jacobi-sobolev Inner Product
Let {Q n (x)}n≥0 denote the sequence of polynomials orthogonal with respect to the non-discrete Sobolev inner product ⟨f, g⟩ = ∫ 1 −1 f(x)g(x)dμα,β(x) + λ ∫ 1 −1 f (x)g(x)dμα+1,β(x) where λ > 0 and dμα,β(x) = (1− x)α(1 + x)βdx with α > −1, β > −1. In this paper we prove a Cohen type inequality for the Fourier expansion in terms of the orthogonal polynomials {Q n (x)}n. Necessary conditions for ...
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