In this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity theorem in Mellin--Bernstein spaces are obtained. The main tool in the proofs is a residue theorem for polar-analytic functions.
Valiron's interpolation formula and a derivative sampling formula in the Mellin setting acquired via polar-analytic functions
Carlo Bardaro;Ilaria Mantellini;
2020
Abstract
In this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity theorem in Mellin--Bernstein spaces are obtained. The main tool in the proofs is a residue theorem for polar-analytic functions.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
