2 citations · 3 across the 9 of their papers we have counts for
9 papers
A residue theorem for polar analytic functions and Mellin analogues of Boas' differentiation formula and Valiron's sampling formula
Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini +1
In this paper, we continue the study of the polar analytic functions, a notion introduced in \cite{BBMS1} and successfully applied in Mellin analysis. Here we obtain another versio…
Development of a complex function theory upon a new concept of polar-analytic functions; Extended version
Carlo Bardaro, Paul. L. Butzer, Ilaria Mantellini +1
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper…
Quadrature formulae for the positive real axis in the setting of Mellin analysis: Sharp error estimates in terms of the Mellin distance
Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini +1
The general Poisson summation formula of Mellin analysis can be considered as a quadrature formula for the positive real axis with remainder. For Mellin bandlimited functions it be…
A fresh approach to the Paley-Wiener theorem for Mellin transforms and the Mellin-Hardy spaces
Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini +1
Here we give a new approach to the Paley--Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is ba…
A generalization of the exponential sampling series and its approximation properties
Carlo Bardaro, Loris Faina, Ilaria Mantellini
Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreo…
Multivariate semi-discrete sampling type operators: pointwise approximation properties
Carlo Bardaro, Ilaria Mantellini
In this paper multivariate extension of the generalized Durrmeyer sampling type series are considered. We establish a Voronovskaja type formula and a quantitative version. Finally…
Mellin Analysis and its distance concept. Applications to sampling theory
Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini +1
In this paper a notion of functional "distance" in the Mellin transform setting is introduced and a general representation formula is obtained for it. Also, a determination of the…
On the Paley-Wiener theorem in the Mellin transform setting
Carlo Bardaro, Paul L. Butzer, Ilaria Mantellini +1
In this paper we establish a version of the Paley-Wiener theorem of Fourier analysis in the frame of the Mellin transform. We provide two different proofs, one involving complex an…
The foundations of fractional Mellin transform analysis
Paul Leo Butzer, Carlo Bardaro, Ilaria Mantellini
In this article we study the basic theoretical properties of Mellin-type fractional integrals, known as generalizations of the Hadamard-type fractional integrals. We give a new app…