From Toeplitz Eigenvalues through Green's Kernels to Higher-Order Wirtinger-Sobolev Inequalities

Details From Toeplitz Eigenvalues through Green's Kernels to Higher-Order Wirtinger-Sobolev Inequalities From Toeplitz Eigenvalues through Green's Kernels to Higher-Order Wirtinger-Sobolev Inequalities

2004-12-14

arxiv.org/abs/math/0412269v1

Mathematics

Functional Analysis

14 pages, LaTeX

Scientific paper

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.

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