From Toeplitz Eigenvalues through Green’s Kernels to Higher-order Wirtinger-Sobolev Inequalities

By Albrecht Böttcher, Harold Widom. 2004

61 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/47c9d770f58a64c5d7fa204cb9d1df6baafcd740

Citations in the corpus

• Generalized locally Toeplitz sequences : Theory and applications (2017, unknown): “264] implies that limn→∞ nλmin(Tn((2−2 cos θ)η))) = K(2η); hence,K(2η) coincides with the constant cη of [26].”