Asymptotic gcd and divisible sequences for entire functions

Interpolating and Sampling Sequences for Entire Functions

We characterise interpolating and sampling sequences for the spaces of entire functions f such that fe ∈ L(C), p ≥ 1 (and some related weighted classes), where φ is a subharmonic weight whose Laplacian is a doubling measure. The results are expressed in terms of some densities adapted to the metric induced by ∆φ. They generalise previous results by Seip for the case φ(z) = |z|2, and by Berndtss...

On GCD-morphic sequences

This note is a response to one of the problems posed by Kwa´sniewski in [1, 2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic sequence F is at the point product of primary GCD-morphic sequences and any GCD-morphic sequence is encoded by natural number valued sequence satisfying condition (C1). The problem of general importance-for example in number theory was formulate...

The Asymptotic Developments of a Class of Entire Functions

Weighted Gcd-Sum Functions

We investigate weighted gcd-sum functions, including the alternating gcd-sum function and those having as weights the binomial coefficients and values of the Gamma function. We also consider the alternating lcm-sum function.

Modeling of ‎I‎nfinite Divisible Distributions Using Invariant and Equivariant Functions

‎Basu’s theorem is one of the most elegant results of classical statistics‎. ‎Succinctly put‎, ‎the theorem says‎: ‎if T is a complete sufficient statistic for a family of probability measures‎, ‎and V is an ancillary statistic‎, ‎then T and V are independent‎. ‎A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics‎. ‎In addition ...