Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions
نویسندگان
چکیده
A Pick function of d variables is a holomorphic map from Πd to Π, where Π is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series ∑∞ n=1 ρnz −n with real numbers ρn that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences {ρn} can occur. We give an extension of Hamburger’s results to Pick functions of two variables.
منابع مشابه
On Positive Harmonic Functions in Cones and Cylinders
We first consider a question raised by Alexander Eremenko and show that if Ω is an arbitrary connected open cone in Rd , then any two positive harmonic functions in Ω that vanish on ∂Ω must be proportional -an already known fact when Ω has a Lipschitz basis or more generally a John basis. It is also shown however that when d ≥ 4, there can be more than one Martin point at infinity for the cone ...
متن کاملMalware Detection using Classification of Variable-Length Sequences
In this paper, a novel method based on the graph is proposed to classify the sequence of variable length as feature extraction. The proposed method overcomes the problems of the traditional graph with variable length of data, without fixing length of sequences, by determining the most frequent instructions and insertion the rest of instructions on the set of “other”, save speed and memory. Acco...
متن کاملAn Inductive Julia-carathéodory Theorem for Pick Functions in Two Variables
We study the asymptotic behavior of Pick functions, analytic functions which take the upper half plane to itself. We show that if a two variable Pick function f has real residues to order 2N − 1 at infinity and the imaginary part of the remainder between f and this expansion is of order 2N + 1, then f has real residues to order 2N and directional residues to order 2N + 1. Furthermore, f has rea...
متن کاملINCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY
We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...
متن کاملNon-local Tug-of-war and the Infinity Fractional Laplacian
Motivated by the “tug-of-war” game studied in [12], we consider a “non-local” version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of flipping a coin in order to decide which direction to choose and then moving of a fixed amount > 0 (as is done in the classical case), it is a s-stable Levy process which chooses at the same time bot...
متن کامل