1,721,100 research outputs found
Functions of Exponential Growth in a Half-Plane, Sets of Uniqueness, and the Müntz–Szász Problem for the Bergman Space
No full textWe introduce and study some new spaces of holomorphic functions on the right half-plane (Formula presented.) In a previous work, S. Krantz, C. Stoppato, and the first named author formulated the Müntz–Szász problem for the Bergman space, that is, the problem to characterize the sets of complex powers (Formula presented.) with (Formula presented.) that form a complete set in the Bergman space (Formula presented.) where (Formula presented.) In this paper, we construct a space of holomorphic functions on the right half-plane, that we denote by (Formula presented.) whose sets of uniqueness (Formula presented.) correspond exactly to the sets of powers (Formula presented.) that are a complete set in (Formula presented.) We show that (Formula presented.) is a reproducing kernel Hilbert space, and we prove a Paley–Wiener-type theorem and several other structural properties. We determine both a necessary and a sufficient condition on a set (Formula presented.) to be a set of uniqueness for (Formula presented.) thus providing a condition for the solution of the Müntz–Szász problem for the Bergman space. Finally, we prove that the orthogonal projection is unbounded on (Formula presented.) for all (Formula presented.
On some spaces of holomorphic functions of exponential growth on a half-plane
Full text linkIn this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression on [0, +∞). We obtain a Paley–Wiener theorem for M2ω, and consequentely the expression for its reproducing kernel. We study the growth of functions in such space and in particular show that Mpω contains functions of order 1. Moreover, we prove that the orthogonal projection from Lp(R,dω) into Mpω is unbounded for p ≠ 2. Furthermore, we compare the spaces Mpω with the classical Hardy and Bergman spaces, and some other Hardy– Bergman-type spaces introduced more recently
On the stability of multidimensional convexity under interpolation
No full textThe relations between the k-uniform convexity of Banach spaces and both the real and the complex method of interpolation are studied. Estimates on the behaviour of the moduli of k-rotundity are given
Alfabeti per l’Osseto. Brevi cenni
No full textThe article provides a short historical overview on some attempts to write down Ossetic sounds by means of different alphabets (§ 1-3). Most often than not, the use of Greek or Latin letters reflects Christian traditions before the Mongol invasion of the North Caucasus or is the product of the curiosity of writers and travellers, who were impressed by the linguistic variety of the region and registered some words and/or sentences. Further, the major phases in the development of a more or less coherent writing system is briefly described. The primary reason for the development of an Ossetic alphabet, based on the Church Slavonic cyrillic script (§ 4) or Georgian xucuri (§ 5), was the goal of the missionaries, coming from Russian and Georgia during the last decades of the 18th and the first half of the following century, to convert Ossetic people to Christianity. Parallel to the process of spreading the Christian faith, a new graphic system, based on Russian cyrillic, was introduced in 1844 (§ 6) and further developed and improved (§ 8). After the October Revolution, the latinization campaign carried out by the bolsheviks involved a shift to a Latin-based alphabet (§ 9), which was again replaced by a new system adapted from the reformed Russian cyrillic orthography in 1938 (§ 10). The transcription system adopted by a German linguist in the 19th century (§ 7), as well as the short experience of using the Georgian civil alphabet (mxedruli) in South Ossetia from 1938 to 1954 (§ 10), clearly reveal an almost perfect coincidence between Ossetic and Georgian with regard to the number and nature of phonemes. The choise of an alphabet, however, depends on cultural, political and ideological orientation more than on purely linguistic considerations, and Ossetic does not represent an exception to this rule
Strongly subharmonic functions, graphs, and their asymptotic growth
No full textLet G be an infinite connected graph with uniformly bounded vertex degree, and let denote the Laplace operator corresponding to the simple random walk on it. In this paper we obtain relations between the structure of the graph and the qualitative behaviour of the class of functions u satisfying ub>0, namely we relate the asymptotic growth of the function u and that of the cardinality of balls in G
Ahlfors regular spaces have regular subspaces of any dimension
Full text linkWe characterize Q-dimensional Ahlfors regular spaces among trees’ boundaries and show how to construct, for each 0 < α < Q, an α-regular subspace. As an application, we give an alternative simple proof of the existence of α-regular subspaces of a Q-dimensional complete Ahlfors regular metric space (X, ρ), which was proved in [8]
Brownian motion and harmonic functions on Sol(p,q)
No full textThe Lie group Sol(p, q) is the semidirect product induced by the action of R on R-2 which is given by (x, y) bar right arrow (e(pz)x, e(-qz)y), z is an element of R. Viewing Sol(p, q) as a three-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with drift. We derive a central limit theorem and compute the rate of escape. Also, we introduce the natural geometric compactification of Sol(p, q) and explain how Brownian motion converges almost surely to the boundary in the resulting topology. We also study all positive harmonic functions for the Laplacian with drift, and determine explicitly all minimal harmonic functions. All these are carried out with a strong emphasis on understanding and using the geometric features of Sol(p, q), and, in particular, the fact that it can be described as the horocyclic product of two hyperbolic planes with curvatures -p(2) and -q(2), respectively
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