Exponential functions in prime characteristic

In this note we determine all power series F(X)\in 1+X\F_p[[X]] such that $(F(X+Y))^{-1} F(X)F(Y)$ has only terms of total degree a multiple of $p$. Up to a scalar factor, they are all the series of the form $F(X)=E_p(cX)\cdot G(X^p)$ for some c\in\F_p and G(X)\in 1+X\F_p[[X]], where $E_p(X)=\exp\big(\sum_{i=0}^{\infty}X^{p^i}/p^i\big)$ is the Artin-Hasse exponential.Comment: 6 pages, to be published in Aequationes Mat

Twisted characteristic pp zeta functions

We propose a "twisted" variation of zeta functions introduced by David Goss in 1979

Rational characteristic functions and markov chains

Abstract 1 We investigate in this paper how to estimate the density function of a random variable using a parametric ARMA model for its characteristic function. The choice of this model is motivated by the fact that this type of density characterizes the duration of staying at an N-states Markov chain, but the approach is general enough to be applied to many practical problems. Both ML and moment-based linear estimates are derived, the former being based on the optimization of a highly non-linear function. 1.Peer ReviewedPostprint (published version

Characteristic functions and joint invariant subspaces

Let T:=[T_1,..., T_n] be an n-tuple of operators on a Hilbert space such that T is a completely non-coisometric row contraction. We establish the existence of a "one-to-one" correspondence between the joint invariant subspaces under T_1,..., T_n, and the regular factorizations of the characteristic function associated with T. In particular, we prove that there is a non-trivial joint invariant subspace under the operators T_1,..., T_n, if and only if there is a non-trivial regular factorization of the characteristic function. We also provide a functional model for the joint invariant subspaces in terms of the regular factorizations of the characteristic function, and prove the existence of joint invariant subspaces for certain classes of n-tuples of operators. We obtain criterions for joint similarity of n-tuples of operators to Cuntz row isometries. In particular, we prove that a completely non-coisometric row contraction T is jointly similar to a Cuntz row isometry if and only if the characteristic function of T is an invertible multi-analytic operator.Comment: 35 page