arXiv subjects

A. D. Hemery

Publications and source records attributed to A. D. Hemery.

2 recordsLinked to original sources

arXiv2011

Zeroes of Wronskians of Hermite polynomials and Young diagrams

For a certain class of partitions, a simple qualitative relation is observed between the shape of the Young diagram and the pattern of zeroes of the Wronskian of the corresponding Hermite polynomials. In the case of two-term Wronskian $W(H_n, H_{n+k})$ we give an explicit formula for the asymptotic shape of the zero set as $n \rightarrow \infty$. Some empirical asymptotic formulas are given for the zero sets of three and four-term Wronskians.

math-ph↗

arXiv2009

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.

math.SP↗