L∞ convergence of interpolation and associated product integration for exponential weights
نویسندگان
چکیده
منابع مشابه
Mean convergence of Lagrange interpolation for Freud’s weights with application to product integration rules
The connection between convergence of product integration rules and mean convergence of Lagrange interpolation in L, (1 <p < 00) has been thoroughly analysed by Sloan and Smith [37]. Motivated by this connection, we investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials associated with Freud weights on R. Our results apply to the weights exp(-x”/2), m = 2,...
متن کاملHermite and Hermite-fejér Interpolation of Higher Order and Associated Product Integration for Erdős Weights
Using the results on the coefficients of Hermite-Fejér interpolations in [5], we investigate convergence of Hermite and Hermite-Fejér interpolation of order m, m = 1, 2, . . . in Lp(0 < p < ∞) and associated product quadrature rules for a class of fast decaying even Erdős weights on the real line.
متن کاملPointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights
For a general class of exponential weights on the line and on (−1, 1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near ±∞ (Freud weights), even weights of faster than smooth polynomial decay near ±∞ (Erdős weights) and even weights which vanish strongly near ±1, for example Pollaczek type weights. 1991...
متن کاملPositive Interpolation Operators with Exponential-Type Weights
Hee Sun Jung and Ryozi Sakai 1 Department of Mathematics Education, Sungkyunkwan University, Seoul 110-745, Republic of Korea 2Department of Mathematics, Meijo University, Nagoya 468-8502, Japan Correspondence should be addressed to Hee Sun Jung; [email protected] Received 26 December 2012; Accepted 7 March 2013 Academic Editor: Roberto Barrio Copyright © 2013 H. S. Jung and R. Sakai. This is an ...
متن کاملQuadrature Sums and Lagrange Interpolation for General Exponential Weights
where > 0. Once the theory had been developed in its entirety, it became clear that one could simultaneously treat not only weights like those above, but also not necessarily even weights on a general real interval. See [3], [12], [16] for various perspectives on this type of potential theory and its applications. One important application is to Lagrange interpolation. Mean convergence of Lagra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2003
ISSN: 0021-9045
DOI: 10.1016/s0021-9045(02)00020-5