scholarly journals On an Identity Theorem in the Nevanlinna Class N

1994 ◽  
Vol 77 (2) ◽  
pp. 184-190 ◽  
Author(s):  
N. Danikas
Keyword(s):  
Nevanlinna Class ◽  
Identity Theorem

Zero Varieties for the Nevanlinna Class in Convex Domains of Finite Type in \Bbb C n

1998 ◽  
Vol 147 (2) ◽  
pp. 391 ◽  
Author(s):  
Joaquim Bruna ◽  
Philippe Charpentier ◽  
Yves Dupain
Keyword(s):  
Finite Type ◽  
Convex Domains ◽  
Nevanlinna Class

scholarly journals A note on the phase retrieval of holomorphic functions

2020 ◽  
pp. 1-8
Author(s):  
Rolando Perez
Keyword(s):  
Unit Circle ◽  
Connected Domain ◽  
Unit Disc ◽  
Phase Retrieval ◽  
Holomorphic Functions ◽  
Nevanlinna Class

Abstract We prove that if f and g are holomorphic functions on an open connected domain, with the same moduli on two intersecting segments, then $f=g$ up to the multiplication of a unimodular constant, provided the segments make an angle that is an irrational multiple of $\pi $ . We also prove that if f and g are functions in the Nevanlinna class, and if $|f|=|g|$ on the unit circle and on a circle inside the unit disc, then $f=g$ up to the multiplication of a unimodular constant.

scholarly journals Valiron’s Interpolation Formula and a Derivative Sampling Formula in the Mellin Setting Acquired via Polar-Analytic Functions

2020 ◽  
Vol 20 (3-4) ◽  
pp. 629-652
Author(s):  
Carlo Bardaro ◽  
Paul L. Butzer ◽  
Ilaria Mantellini ◽  
Gerhard Schmeisser
Keyword(s):  
Analytic Functions ◽  
Main Tool ◽  
Interpolation Formula ◽  
Residue Theorem ◽  
Differentiation Formula ◽  
Sampling Formula ◽  
Bernstein Spaces ◽  
Derivative Sampling ◽  
Classical Interpolation ◽  
Identity Theorem

AbstractIn 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.

COMPARING AND ZILBER’S EXPONENTIAL FIELDS: ZERO SETS OF EXPONENTIAL POLYNOMIALS

2014 ◽  
Vol 15 (1) ◽  
pp. 71-84 ◽  
Author(s):  
P. D’Aquino ◽  
A. Macintyre ◽  
G. Terzo
Keyword(s):  
Analytic Function ◽  
Function Theory ◽  
Research Programme ◽  
Exponential Functions ◽  
Exponential Polynomials ◽  
Zero Sets ◽  
Diophantine Geometry ◽  
Complex Exponential ◽  
Identity Theorem

We continue the research programme of comparing the complex exponential with Zilberś exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for $\mathbb{C}$ using analytic function theory, for example, the Identity Theorem.

Boundary behaviour of functions of Nevanlinna class

2004 ◽  
Vol 53 (2) ◽  
pp. 347-396 ◽  
Author(s):  
A. Bourhim ◽  
O. El-Fallah ◽  
K. Kellay
Keyword(s):  
Boundary Behaviour ◽  
Nevanlinna Class
Sign in / Sign up

Export Citation Format

Share Document