scholarly journals Weighted Frechet spaces of entire functions from the class of power series spaces of finite type

2013 ◽  
Author(s):  
П.С. Сергунин ◽  
А.В. Абанин ◽  
Ч.Т. Фам
Keyword(s):  
Power Series ◽  
Finite Type ◽  
Entire Functions ◽  
Fréchet Spaces

Изучаются весовые пространства Фреше целых функций, задаваемые весовыми последовательностями общего вида. Получены достаточные условия на веса, при которых они обладают топологическими инвариантами Фогта - Вагнера, и, таким образом, относятся к классу пространств степенных рядов конечного типа.

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

Weak-Star Continuous Analytic Functions

1995 ◽  
Vol 47 (4) ◽  
pp. 673-683 ◽  
Author(s):  
R. M. Aron ◽  
B. J. Cole ◽  
T. W. Gamelin
Keyword(s):  
Unit Ball ◽  
Finite Type ◽  
Analytic Functions ◽  
Approximation Property ◽  
Entire Functions ◽  
Open Unit ◽  
Closed Unit Ball ◽  
Open Unit Ball ◽  
Weakly Continuous ◽  
Weak Star

AbstractLet 𝒳 be a complex Banach space, with open unit ball B. We consider the algebra of analytic functions on B that are weakly continuous and that are uniformly continuous with respect to the norm. We show these are precisely the analytic functions on B that extend to be weak-star continuous on the closed unit ball of 𝒳**. If 𝒳* has the approximation property, then any such function is approximable uniformly on B by finite polynomials in elements of 𝒳*. On the other hand, there exist Banach spaces for which these finite-type polynomials fail to approximate. We consider also the approximation of entire functions by finite-type polynomials. Assuming 𝒳* has the approximation property, we show that entire functions are approximable uniformly on bounded sets if and only if the spectrum of the algebra of entire functions coincides (as a point set) with 𝒳**.

scholarly journals Power series spaces $Λ_{k}(a)$ of finite type and related nuclearities

1975 ◽  
Vol 53 (1) ◽  
pp. 1-13 ◽  
Author(s):  
M. Ramanujan ◽  
T. Terzioglu
Keyword(s):  
Power Series ◽  
Finite Type

Entire Functions Defined by Certain Power Series

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

scholarly journals Positioning matrices with respect to the boundary of the maximal group

1986 ◽  
Vol 33 (1) ◽  
pp. 113-122
Author(s):  
J. DeFranza ◽  
D.J. Fleming
Keyword(s):  
Power Series ◽  
Banach Algebra ◽  
Finite Type ◽  
Maximal Group ◽  
Nörlund Means ◽  
Invertible Elements

Let Δ denote the Banach algebra of all conservative triangular matrics, M the maximal group of invertible elements of Δ, B the boundary of M and . In this note little Nörlund means are located with respect to the disjoint decomposition M u B u N of Δ in terms of the zeros of the generating power series. Further, corridor matrices of finite type, that is, conservative methods with finitely many convergent diagonals, are located with respect to M u B u N.

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
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