The authors of the title proved in [2] an elegant identity expressing a Toeplitz determinant in terms of the Fredholm determinant of an infinite matrix which (although not described as such) is the product of two Hankel matrices. The proof used combinatorial theory, in particular a theorem of Gessel expressing a Toeplitz determinant as a sum over partitions of products of Schur functions. The p...

Keywords: Squared spherical Bessel functions Regularization of Hankel series Gaussian power-law densities Kummer distributions Airy approximation of Bessel integrals a b s t r a c t Bessel integrals of type R 1 0 k lþ2 e Àak 2 ÀðbþixÞk j 2 l ðpkÞdk are studied, where the squared spherical Bessel function j 2 l is averaged with a modulated Gaussian power-law density. These inte-grals define the ...

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp estimates the first four initial coefficients of this class are addressed. Furthermore, we obtain Fekete–Szegö inequality, sharp upper bounds second and third Hankel determinants, logarithmic coefficients, third-order determinants two...

We prove the H-infinity error bounds for Lyapunov balanced truncation and for optimal Hankel norm approximation under the assumption that the Hankel operator is nuclear. This is an improvement of the result from Glover, Curtain, and Partington [SIAM J. Control Optim., 26 (1998), pp. 863–898], where additional assumptions were made. The proof is based on convergence of the Schmidt pairs of the H...

We study a super group of the group of Riordan arrays, where the elements of the group are given by a triple of power series. We show that certain subsets are subgroups, and we identify a normal subgroup whose cosets correspond to Riordan arrays. We give an example of an almost-Riordan array that has been studied in the context of Hankel and Hankel plus Toepliz matrices, and we show that suitab...

A classification of Hankel determinant solutions of the restricted Toda chain equations is presented through polynomial Ansatz for moments. Each solution corresponds to the Sheffer class orthogonal polynomials. In turn, these solutions are equivalent to solutions with separated variables in Toda chain. These solutions lead naturally to explicit Hankel determinants of some combinatorial numbers.

The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient conditions to sum the Walsh–Fourier series of a function of bounded variation. 2013 Elsevier Inc. All rights reserved.