Dergiler / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 6
A Cohen type inequality for Laguerre--Sobolev expansions with a mass point outside their oscillatory regime
- Sayfa
- 994–1006
- DOI
- —
Özet
Let consider the Sobolev type inner product \langle f, g\rangleS = \int0\infty f(x)g(x)d m (x) + Mf(c)g(c) + Nf\prime(c) g\prime(c), where dm (x) = xa e-xdx, a > -1, is the Laguerre measure, c < 0, and M, N \geq 0. In this paper we get a Cohen-type inequality for Fourier expansions in terms of the orthonormal polynomials associated with the above Sobolev inner product. Then, as an immediate consequence, we deduce the divergence of Fourier expansions and Cesàro means of order d in terms of this kind of Laguerre--Sobolev polynomials.
Abstract
Let consider the Sobolev type inner product \langle f, g\rangleS = \int0\infty f(x)g(x)d m (x) + Mf(c)g(c) + Nf\prime(c) g\prime(c), where dm (x) = xa e-xdx, a > -1, is the Laguerre measure, c < 0, and M, N \geq 0. In this paper we get a Cohen-type inequality for Fourier expansions in terms of the orthonormal polynomials associated with the above Sobolev inner product. Then, as an immediate consequence, we deduce the divergence of Fourier expansions and Cesàro means of order d in terms of this kind of Laguerre--Sobolev polynomials.