1 citations · 1 across the 6 of their papers we have counts for
6 papers
Complex hyper-power series and generalized complex analytic functions
Sekar Nugraheni, Paolo Giordano
This paper studies the equivalence between generalized holomorphic functions (GHF) and complex analytic functions in the framework of Robinson-Colombeau generalized numbers. In eve…
Classical finite dimensional fixed point methods for generalized functions
Kevin Islami, George Apaaboah, Paolo Giordano
We prove Banach, Newton-Raphson and Brouwer fixed point theorems in the framework of generalized smooth functions, a minimal extension of Colombeau's theory (and hence of classical…
Dirac delta as a generalized holomorphic function
Sekar Nugraheni, Paolo Giordano
The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of…
The Hahn-Banach theorem in spaces of nonlinear generalized functions
Djamel eddine Kebiche, Paolo Giordano
In this paper, we establish a suitable version of the Hahn-Banach theorem within the framework of Colombeau spaces, a class of spaces used to model generalized functions. Our appro…
Universal properties of spaces of generalized functions
Djamel eddine Kebiche, Paolo Giordano
By means of several examples, we motivate that universal properties are the simplest way to solve a given mathematical problem, explaining in this way why they appear everywhere in…
A Grothendieck topos of generalized functions I: basic theory
Paolo Giordano, Michael Kunzinger, Hans Vernaeve
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions define…