Related papers: Some open questions in analysis for Dirichlet seri…
This paper presents a number of identities for Dirichlet series and series with Stirling numbers of the first kind. As coefficients for the Dirichlet series we use Cauchy numbers of the first and second kinds, hyperharmonic numbers,…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
We consider Dirichlet p-branes in type II string theory on a space which has been toroidally compactified in d dimensions. We give an explicit construction of the field theory description of this system by putting a countably infinite…
We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…
We do research on the real method of Hardy spaces associated with the Dunkl setting on the real line for the range of 0<p<=1.
Following ideas from a preprint of the second author, see [2], we investigate relations of dynamical Teichmuller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and…
The paper deals with the Dirichlet problem for the nonstationary Stokes system in a cone. The authors obtain existence and uniqueness results for solutions in weighted Sobolev spaces and study the asymptotics of the solutions at infinity.
We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of…
Associated to the class of restricted-weak type weights for the Hardy operator, we find a new class of Lorentz spaces for which the normability property holds. This result is analogous to the characterization given by Sawyer for the…
The Hardy spaces of Dirichlet series denoted by ${\cal H}^p$ ($p\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two…
We give a broad overview of superstring duality, Dirichlet branes, and some implications of both for questions about the structure of space-time at short distances.
In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some…
We give an overview of parts of the theory of Hardy spaces from the viewpoint of signals and systems theory. There are books on this topic, which dates back to Bode, Nyquist, and Wiener, and that eventually led to the developement of…
In the authors' first paper, Beurling-Rudin-Korenbljum type characterization of the closed ideals in a certain algebra of holomorphic functions was used to describe the lattice of invariant subspaces of the shift plus a complex Volterra…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
A few years ago, the concept of a D-analogue was introduced as a Dirichlet series analogue for the already known and well researched hypergeometric q-series. The D-analogue of the q-Dixon sum is given here, in the context of seeing a direct…
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of…
We explore a function theory connected with the principal series representation of SL(2,R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy…
A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorem. As a corollary we describe the almost-invariant…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…