arXiv subjects

A. Boettcher

Publications and source records attributed to A. Boettcher.

5 recordsLinked to original sources

arXiv2007

Increase of the mean inner Coulomb potential in Au clusters induced by surface tension and its implication for electron scattering

Electron holography in a transmission electron microscope was applied to measure the phase shift induced by Au clusters as a function of the cluster size. Large phase shifts Df observed for small Au clusters cannot be described by the well-known equation Df=C_E V_0 t (C_E: interaction constant, V_0: mean inner Coulomb potential (MIP) of bulk gold, t: cluster thickness). The rapid increase of the Au MIP with decreasing cluster size derived from Df, can be explained by the compressive strain of surface atoms in the cluster.

cond-mat.mtrl-sci↗

arXiv2006

Szegö via Jacobi

At present there exist numerous different approaches to results on Toeplitz determinants of the type of Szegö's strong limit theorem. The intention of this paper is to show that Jacobi's theorem on the minors of the inverse matrix remains one of the most comfortable tools for tackling the matter. We repeat a known proof of the Borodin-Okounkov formula and thus of the strong Szegö limit theorem that is based on Jacobi's theorem. We then use Jacobi's theorem to derive exact and asymptotic formulas for Toeplitz determinants generated by functions with nonzero winding number. This derivation is new and completely elementary

math.FA↗

arXiv2004

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

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.

math.FA↗

arXiv2001

On the determinant formulas by Borodin, Okounkov, Baik, Deift, and Rains

We give alternative proofs to (block case versions of) some formulas for Toeplitz and Fredholm determinants established recently by the authors of the title. Our proof of the Borodin-Okounkov formula is very short and direct. The proof of the Baik-Deift-Rains formulas is based on standard manipulations with Wiener-Hopf factorizations.

math.FA↗

arXiv2000

One more proof of the Borodin-Okounkov formula for Toeplitz determinants

Recently, Borodin and Okounkov established a remarkable identity for Toeplitz determinants. Two other proofs of this identity were subsequently found by Basor and Widom, who also extended the formula to the block case. We here give one more proof, also for the block case. This proof is based on a formula for the inverse of a finite block Toeplitz matrix obtained in the late seventies by Silbermann and the author.

math.FA↗