Zeros of sections of power series representing entire functions admissible in the sense of Hayman

1983 ◽  
pp. 19-35 ◽  
Author(s):  
Albert Edrei
Keyword(s):  
Power Series ◽  
Entire Functions ◽  
Sections Of Power Series

scholarly journals Mackey-complete spaces and power series – a topological model of differential linear logic

2016 ◽  
Vol 28 (4) ◽  
pp. 472-507 ◽  
Author(s):  
MARIE KERJEAN ◽  
CHRISTINE TASSON
Keyword(s):  
Power Series ◽  
Vector Space ◽  
Topological Vector Space ◽  
Taylor Expansion ◽  
Entire Functions ◽  
Linear Logic ◽  
Quantitative Model ◽  
Linear Functions ◽  
Topological Model ◽  
Bounded Linear

In this paper, we describe a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted as bounded linear functions. So as to interpret non-linear proofs of Linear Logic, we use a notion of power series between Mackey-complete spaces, generalizing entire functions in $\mathbb{C}$. Finally, we get a quantitative model of Intuitionist Differential Linear Logic, with usual syntactic differentiation and where interpretations of proofs decompose as a Taylor expansion.

Universality properties of the quaternionic power series and entire functions

2015 ◽  
Vol 288 (8-9) ◽  
pp. 917-924 ◽  
Author(s):  
Sorin G. Gal ◽  
Irene Sabadini
Keyword(s):  
Power Series ◽  
Entire Functions

Entire Functions Defined by Certain Power Series

1926 ◽  
Vol 27 (3) ◽  
pp. 209
Author(s):  
Julia T. Colpitts
Keyword(s):  
Power Series ◽  
Entire Functions

SECTIONS OF POWER SERIES OF MATRIX-VALUED SCHUR FUNCTIONS

Analysis ◽  
1992 ◽  
Vol 12 (3-4) ◽  
pp. 343-358
Author(s):  
Bernd Fritzsche ◽  
Bernd Kirstein
Keyword(s):  
Power Series ◽  
Schur Functions ◽  
Sections Of Power Series

scholarly journals Universal entire functions with gap power series

1998 ◽  
Vol 9 (4) ◽  
pp. 529-536 ◽  
Author(s):  
Wolfgang Luh ◽  
Valeri A. Martirosian ◽  
Jürgen Müller
Keyword(s):  
Power Series ◽  
Entire Functions

scholarly journals Analogues of Whittker's theorem for Laplace-Stieltjes integrals

2016 ◽  
Vol 8 (2) ◽  
pp. 239-250
Author(s):  
M.S. Dobushovskyy ◽  
M.M. Sheremeta
Keyword(s):  
Power Series ◽  
Entire Functions ◽  
Stieltjes Integral

For the maximum of the integrand of Laplace-Stieltjes integral the lower estimates on sequence are found. Using the estimates we obtained analogues of Whittaker's theorem for entire functions given by lacunary power series.

scholarly journals U-Operators

2005 ◽  
Vol 78 (1) ◽  
pp. 59-90 ◽  
Author(s):  
L. Bernal-González ◽  
J. A. Prado-Tendero
Keyword(s):  
Power Series ◽  
Complex Plane ◽  
Entire Functions ◽  
Shift Operators ◽  
Compact Subsets

AbstractInspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain compact subsets of the complex plane or of, respectively, the punctured complex plane, we introduce in this paper the new concept of U-operators, which are defined on the space of entire functions. Concrete examples, including differential and antidifferential operators, composition, multiplication and shift operators, are studied. A result due to Luh, Martirosian and Müller about the existence of universal entire functions with gap power series is also strengthened.

INTERPRETING ARITHMETIC IN THE FIRST-ORDER THEORY OF ADDITION AND COPRIMALITY OF POLYNOMIAL RINGS

2019 ◽  
Vol 84 (3) ◽  
pp. 1194-1214
Author(s):  
JAVIER UTRERAS
Keyword(s):  
Power Series ◽  
Entire Functions ◽  
Order Theory ◽  
Ring Structure ◽  
Polynomial Rings ◽  
Series Ring ◽  
First Order ◽  
First Order Theory ◽  
Power Series Rings ◽  
Image Position

AbstractWe study the first-order theory of polynomial rings over a GCD domain and of the ring of formal entire functions over a non-Archimedean field in the language $\{ 1, + , \bot \}$. We show that these structures interpret the first-order theory of the semi-ring of natural numbers. Moreover, this interpretation depends only on the characteristic of the original ring, and thus we obtain uniform undecidability results for these polynomial and entire functions rings of a fixed characteristic. This work enhances results of Raphael Robinson on essential undecidability of some polynomial or formal power series rings in languages that contain no symbols related to the polynomial or power series ring structure itself.

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