- Turkish Journal of Mathematics
- Vol: 38 Issue: 6
- A Cohen type inequality for Laguerre--Sobolev expansions with a mass point outside their oscillatory...
A Cohen type inequality for Laguerre--Sobolev expansions with a mass point outside their oscillatory regime
Authors : Edmundo José Huertas Cejudo, Francisco Marcellán Español, Maria Francisca Perez Valero, Yamilet Quintana
Pages : 994-1006
Doi:10.3906/mat-1312-2
View : 9 | Download : 10
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Sobolev-type orthogonal polynomials, Cohen-type inequality, Fourier--Sobolev expansions