On some spaces of holomorphic functions of exponential growth on a half-plane

Abstract

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by M p ! , whose growth conditions are given in terms of a translation invariant measure ! on the closed half-plane R. Such a measure has the form ! D ˝m, where m is the Lebesgue measure on R and is a regular Borel measure on OE0; C1/. We call these spaces generalized Hardy-Bergman spaces on the half-plane R.We study in particular the case of purely atomic, with point masses on an arithmetic progression on OE0; C1/. We obtain a Paley-Wiener theorem for M 2 ! , and consequentely the expression for its reproducing kernel. We study the growth of functions in such space and in particular show that M

Holomorphic function spaces on homogeneous Siegel domains

“…It was shown in [68] that the space A 2,2 µ (C + ) contains wildly behaved functions, such as exp(ie 2πiz ). See also [69] and references therein for a further discussion on functions in A 2,2 µ (C + ) for a general µ.…”

Holomorphic Function Spaces on Homogeneous Siegel Domains

“…It was shown in [51] that the space A 2,2 µ (C + ) contains wildly behaved functions, such as exp(ie 2πiz ). See also [52] and references therein for a further discussion on functions in A 2,2 µ (C + ) for a general µ.…”

The structure of the fractional powers of the noncommutative Fourier law

“…The case of spectral operators has, for instance, been studied in Gantner, 42 and the theory of groups and semigroups of quaternionic linear operators has been studied in Alpay et al, 43,44 Colombo and Sabadini, 45 and Ghiloni and Recupero. 46 We are now interested in developing ideas from one and several complex variables, such as in previous studies, 16,[47][48][49][50][51][52][53][54][55] to the quaternionic setting.…”