Turkish Journal of Mathematics
DOI
10.3906/mat-1312-2
Abstract
Let consider the Sobolev type inner product \langle f, g\rangle_S = \int_0^{\infty} f(x)g(x)d \mu (x) + Mf(c)g(c) + Nf^{\prime}(c) g^{\prime}(c), where d\mu (x) = x^{\alpha} e^{-x}dx, \alpha > -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 \delta in terms of this kind of Laguerre--Sobolev polynomials.
Keywords
Sobolev-type orthogonal polynomials, Cohen-type inequality, Fourier--Sobolev expansions
First Page
994
Last Page
1006
Recommended Citation
CEJUDO, EDMUNDO JOSÉ HUERTAS; ESPANOL, FRANCISCO MARCELLÁN; VALERO, MARÍA FRANCISCA PÉREZ; and QUINTANA, YAMILET
(2014)
"A Cohen type inequality for Laguerre--Sobolev expansions with a mass point outside their oscillatory regime,"
Turkish Journal of Mathematics: Vol. 38:
No.
6, Article 5.
https://doi.org/10.3906/mat-1312-2
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss6/5
