Slice Regular Malmquist–Takenaka System in the Quaternionic Hardy Spaces

Extension results for slice regular functions of a quaternionic variable

In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function f at a point q = x + yI can be recovered by the values of f at the points q + yJ and q + yK for any choice of imaginary units I, J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a...

Poles of regular quaternionic functions

This paper studies the singularities of Cullen-regular functions of one quaternionic variable, as defined in [7]. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullenregular functions are thus classified as removable, essential or poles. The quaternionic analogues of meromorphic complex functions, called semiregular functions, turn out to be quotients of Culle...

Hardy spaces for the strip

In this paper we present some new results about the conformally invariant Hardy spaces Hp(S) in the strip S := { z ∈ C | | Imz | < 1 } for 0 < p <∞ . We give an intrinsic characterization of these spaces and we prove that the set of polynomials are dense in all of them.

On the Generalized Hardy Spaces

and Applied Analysis 3 Definition 2.1. Let F : H U → H U be a linear operator such that F f 0 if and only if f 0, that is, F is 1-1. For 1 ≤ p < ∞, the generalized Hardy space HF,p U HF,p is defined to be the collection of all analytic functions f on U for which

Hardy Inequalities in Function Spaces