Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace ...Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace series of f. The special value λ:= (n-2)/2 of δ is known as the critical index. For 0 < δ≤λ, we set p0 := 2λ/(λ+δ). The main aim of this paper is to prove thatwith l > 1.展开更多
Here we discuss some phenomena of equiconvergence for the functions analytic inside the lemniscate. A quantitative estimate of sequences of differences between the Jacobi polynomials and Lagrange interpolants and some...Here we discuss some phenomena of equiconvergence for the functions analytic inside the lemniscate. A quantitative estimate of sequences of differences between the Jacobi polynomials and Lagrange interpolants and some other results are obtained.展开更多
We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.
文摘Let Rn be an n-dimensional Euclidean space with n≥ 3. Denote by Ωn the unit sphere in Rn. For a function f∈L(Ωn) we denote by ENδ(f) the equiconvergent operator of Cesaro means of order δ of the Fourier-Laplace series of f. The special value λ:= (n-2)/2 of δ is known as the critical index. For 0 < δ≤λ, we set p0 := 2λ/(λ+δ). The main aim of this paper is to prove thatwith l > 1.
文摘Here we discuss some phenomena of equiconvergence for the functions analytic inside the lemniscate. A quantitative estimate of sequences of differences between the Jacobi polynomials and Lagrange interpolants and some other results are obtained.
文摘We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.
