On Convergence and Divergence of Fourier Expansions with Respect to Some Gegenbauer-sobolev Type Inner Product

نویسندگان

  • BUJAR XH. FEJZULLAHU
  • FRANCISCO MARCELLÁN
چکیده

Let introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f(x)g(x)dμ(x) + M [f(1)g(1) + f(−1)g(−1)] + N [f ′(1)g′(1) + f ′(−1)g′(−1)],

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 ...

متن کامل

Divergent Legendre-sobolev Polynomial Series

Let be introduced the Sobolev-type inner product (f, g) = 1 2 Z 1 −1 f(x)g(x)dx + M [f ′(1)g′(1) + f ′(−1)g′(−1)], where M ≥ 0. In this paper we will prove that for 1 ≤ p ≤ 4 3 there are functions f ∈ L([−1, 1]) whose Fourier expansion in terms of the orthonormal polynomials with respect to the above Sobolev inner product are divergent almost everywhere on [−1, 1]. We also show that, for some v...

متن کامل

Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f, g)S = 〈f, g〉 + λ〈f ′, g′〉 where 〈f, g〉 = ∫ 1 −1 f(x)g(x)(1 − x 2)α−1/2dx with α > −1/2 and λ > 0. The asymptotics of the zeros and norms of these polynomials is also established. The study of the orthogonal polynomials with respect to the inner products that involve der...

متن کامل

Generalized trace formula and asymptotics of the averaged Turan determinant for polynomials orthogonal with a discrete Sobolev inner product

Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f (x)g(x) d (x)+ K ∑ k=1 Nk ∑ i=0 Mk,if (ak)g (ak), where the mass points ak belong to [−1, 1], and Mk,i > 0(i = 0, 1, . . . , Nk). In this paper, we obtain generalized trace formula and asymptotics of the averagedTuran determinant for the Sobolev-type orthogonal pol...

متن کامل

Research Article A Cohen-Type Inequality for Jacobi-Sobolev Expansions

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 Marke...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008