Differential inequalities on banach spaces of entire functions. II

1992 ◽  
Vol 32 (1) ◽  
pp. 103-109
Author(s):  
S. Norvidas
Keyword(s):  
Banach Spaces ◽  
Entire Functions ◽  
Differential Inequalities

scholarly journals Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 150
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Dimensional Algebra ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Linear Subspaces ◽  
Infinite Dimensional Banach Space

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

Differential inequalities of second oeder in Banach spaces

1975 ◽  
Vol 27 (1) ◽  
pp. 96-99
Author(s):  
V. I. Okhronchuk
Keyword(s):  
Banach Spaces ◽  
Differential Inequalities

scholarly journals Duals of Banach spaces of entire functions

1990 ◽  
Vol 32 (2) ◽  
pp. 215-220 ◽  
Author(s):  
J. M. Anderson ◽  
J. Duncan
Keyword(s):  
Banach Spaces ◽  
Entire Functions ◽  
Positive Function ◽  
Image Position ◽  
Strictly Positive Function

Let w be a strictly positive function on ℂ and let , respectively denote the Banach spaces of those entire functions φ(z) with ∣φ(z)∣= O(w(z)) and ∣φ(z)∣ = o(w(z)). In this generality, these spaces may contain only constants, but for many functions w(z) these will be interesting Banach spaces with norm.We study two specific problems.

scholarly journals Isomorphisms of some algebras of analytic functions of bounded type on Banach spaces

2021 ◽  
Vol 56 (1) ◽  
pp. 106-112
Author(s):  
S.I. Halushchak
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Complex Banach Space ◽  
Homogeneous Polynomials ◽  
Topological Algebras ◽  
Nonlinear Functional

The theory of analytic functions is an important section of nonlinear functional analysis.In many modern investigations topological algebras of analytic functions and spectra of suchalgebras are studied. In this work we investigate the properties of the topological algebras of entire functions,generated by countable sets of homogeneous polynomials on complex Banach spaces. Let $X$ and $Y$ be complex Banach spaces. Let $\mathbb{A}= \{A_1, A_2, \ldots, A_n, \ldots\}$ and $\mathbb{P}=\{P_1, P_2,$ \ldots, $P_n, \ldots \}$ be sequences of continuous algebraically independent homogeneous polynomials on spaces $X$ and $Y$, respectively, such that $\|A_n\|_1=\|P_n\|_1=1$ and $\deg A_n=\deg P_n=n,$ $n\in \mathbb{N}.$ We consider the subalgebras $H_{b\mathbb{A}}(X)$ and $H_{b\mathbb{P}}(Y)$ of the Fr\'{e}chet algebras $H_b(X)$ and $H_b(Y)$ of entire functions of bounded type, generated by the sets $\mathbb{A}$ and $\mathbb{P}$, respectively. It is easy to see that $H_{b\mathbb{A}}(X)$ and $H_{b\mathbb{P}}(Y)$ are the Fr\'{e}chet algebras as well. In this paper we investigate conditions of isomorphism of the topological algebras $H_{b\mathbb{A}}(X)$ and $H_{b\mathbb{P}}(Y).$ We also present some applications for algebras of symmetric analytic functions of bounded type. In particular, we consider the subalgebra $H_{bs}(L_{\infty})$ of entire functions of bounded type on $L_{\infty}[0,1]$ which are symmetric, i.e. invariant with respect to measurable bijections of $[0,1]$ that preserve the measure. We prove that$H_{bs}(L_{\infty})$ is isomorphic to the algebra of all entire functions of bounded type, generated by countable set of homogeneous polynomials on complex Banach space $\ell_{\infty}.$

Differential inequalities and equations in Banach spaces with a cone

2008 ◽  
Vol 69 (1) ◽  
pp. 245-255 ◽  
Author(s):  
Leopold Herrmann
Keyword(s):  
Banach Spaces ◽  
Differential Inequalities

scholarly journals Classical operators on weighted Banach spaces of entire functions

2013 ◽  
Vol 141 (12) ◽  
pp. 4293-4303 ◽  
Author(s):  
María J. Beltrán ◽  
José Bonet ◽  
Carmen Fernández
Keyword(s):  
Banach Spaces ◽  
Entire Functions ◽  
Weighted Banach Spaces
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