From Toeplitz Eigenvalues through Green's Kernels to Higher-Order Wirtinger-Sobolev Inequalities
Functional Analysis
2007-05-23 v1
Abstract
The paper is concerned with a sequence of constants which appear in several problems. These problems include the minimal eigenvalue of certain positive definite Toeplitz matrices, the minimal eigenvalue of some higher-order ordinary differential operators, the norm of the Green kernels of these operators, the best constant in a Wirtinger-Sobolev inequality, and the conditioning of a special least squares problem. The main result of the paper gives the asymptotics of this sequence.
Cite
@article{arxiv.math/0412269,
title = {From Toeplitz Eigenvalues through Green's Kernels to Higher-Order Wirtinger-Sobolev Inequalities},
author = {A. Boettcher and H. Widom},
journal= {arXiv preprint arXiv:math/0412269},
year = {2007}
}
Comments
14 pages, LaTeX