Localized Polynomial Frames on the Interval with Jacobi Weights |
| |
Authors: | Pencho Petrushev Yuan Xu |
| |
Institution: | (1) Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;(2) Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222, USA |
| |
Abstract: | As is well known the kernel of the orthogonal projector onto the polynomials of
degree n in L2(wα,β, −1, 1]), wα,β(t) = (1 − t)α(1 + t)β, can be written in terms of Jacobi polynomials. It is shown that if the coefficients in this kernel are smoothed out by sampling
a compactly supported C∞ function then the resulting function has nearly exponential (faster than any polynomial) rate of decay away from the main
diagonal. This result is used for the construction of tight polynomial frames for L2(wα,β) with elements having almost exponential localization. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|