There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them the short combinatorial proofs they deserve. Our replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tabl...

rticle history: vailable online xxxx eywords: iscrete Hilbert transform iscrete-time analytic signal edrosian product theorem The aim of this paper is to discuss discrete-time analytic signals and to provide the derivation of Bedrosian product theorem for discrete-time Hilbert transform. With the aid of the continuous-time analytic signals we provide a new approach to produce the discretetime a...

The bulk properties of composites are known to depend strongly on the microstructure. This dependence can be quanti ed in terms of a representation introduced by D. Bergman, which factorizes the geometry dependence from the contrast. Based on this analytic representation of the e ective permittivity, we present a general scheme to estimate the micro structural parameters, such as the volume fra...

Fuchsian equations provide a way of constructing large classes of spacetimes whose singularities can be described in detail. In some of the applications of this technique only the analytic case could be handled up to now. This paper develops a method of removing the undesirable hypothesis of analyticity. This is applied to the specific case of the Gowdy spacetimes in order to show that analogue...

We develop the basic elements of a Cauchy theory on the complex Levi-Civita field, which constitutes the smallest algebraically closed nonArchimedean extension of the complex numbers. We introduce a concept of analyticity based on differentiation, and show that it leads to local expandability in power series. We show that analytic functions can be integrated over suitable piecewise smooths path...

In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := −[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space L(Tκ), in such a way that the resulting operator is self-adjoint,...

Results on the analytic behavior of the limiting spectral distribution of matrices of sample covariance type, studied in Marčenko and Pastur [2] and Yin [8], are derived. Through an equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and resembles √ |x− x0| for mo...