scholarly journals The space of scalarly integrable functions for a Fréchet-space-valued measure

2009 ◽  
Vol 354 (2) ◽  
pp. 641-647 ◽  
Author(s):  
R. del Campo ◽  
W.J. Ricker
Keyword(s):  
Fréchet Space ◽  
Frechet Space ◽  
Integrable Functions

scholarly journals THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS

2009 ◽  
Vol 88 (1) ◽  
pp. 49-60 ◽  
Author(s):  
R. DEL CAMPO ◽  
W. J. RICKER
Keyword(s):  
Function Space ◽  
Riesz Space ◽  
Fréchet Space ◽  
Frechet Space ◽  
Function Lattice ◽  
Measurable Functions ◽  
Integrable Functions ◽  
Locally Convex

AbstractGiven a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space L1(ν) of integrable functions with respect to a Fréchet-space-valued measure ν is the space L1w(ν) of scalarly ν-integrable functions. Further consequences are also given.

Darboux chart on projective limit of weak symplectic Banach manifold

2015 ◽  
Vol 12 (07) ◽  
pp. 1550072 ◽  
Author(s):  
Pradip Mishra
Keyword(s):  
Banach Space ◽  
Symplectic Structure ◽  
Reflexive Banach Space ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Banach Manifold ◽  
Boundedness Condition ◽  
Projective System ◽  
Banach Manifolds

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.

scholarly journals Characterizations and properties of graphs of Baire functions

2018 ◽  
Vol 68 (4) ◽  
pp. 789-802
Author(s):  
Balázs Maga
Keyword(s):  
Banach Space ◽  
Topological Space ◽  
Convex Set ◽  
Vertical Section ◽  
Fréchet Space ◽  
Frechet Space ◽  
Similar Question ◽  
Baire Functions

Abstract Let X be a paracompact topological space and Y be a Banach space. In this paper, we will characterize the Baire-1 functions f : X → Y by their graph: namely, we will show that f is a Baire-1 function if and only if its graph gr(f) is the intersection of a sequence $\begin{array}{} \displaystyle (G_n)_{n=1}^{\infty} \end{array}$ of open sets in X × Y such that for all x ∈ X and n ∈ ℕ the vertical section of Gn is a convex set, whose diameter tends to 0 as n → ∞. Afterwards, we will discuss a similar question concerning functions of higher Baire classes and formulate some generalized results in slightly different settings: for example we require the domain to be a metrized Suslin space, while the codomain is a separable Fréchet space. Finally, we will characterize the accumulation set of graphs of Baire-2 functions between certain spaces.

scholarly journals A New Version of the Generalized Krätzel-Fox Integral Operators

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 222 ◽  
Author(s):  
Shrideh Al-Omari ◽  
Ghalib Jumah ◽  
Jafar Al-Omari ◽  
Deepali Saxena
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Convolution Theorem ◽  
Fréchet Space ◽  
Frechet Space ◽  
Generalized Convolution ◽  
Real Numbers ◽  
Convolution Products ◽  
Fox’S H Function ◽  
Krätzel Integral

This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and b > 0 , the Fréchet space H a , b of testing functions has been identified as a subspace of certain Boehmian spaces. To establish the Boehmian spaces, two convolution products and some related axioms are established. The generalized variant of the cited Krätzel-Fox integral operator is well defined and is the operator between the Boehmian spaces. A generalized convolution theorem has also been given.

Interpolation in Separable Frechet Spaces with Applications to Spaces of Analytic Functions

1975 ◽  
Vol 27 (5) ◽  
pp. 1110-1113 ◽  
Author(s):  
Paul M. Gauthier ◽  
Lee A. Rubel
Keyword(s):  
Sufficient Conditions ◽  
Fréchet Space ◽  
Complex Numbers ◽  
Frechet Space ◽  
Fréchet Spaces ◽  
Continuous Linear Functional ◽  
Interpolating Sequence ◽  
Necessary And Sufficient ◽  
Locally Convex ◽  
Spaces Of Analytic Functions

Let E be a separable Fréchet space, and let E* be its topological dual space. We recall that a Fréchet space is, by definition, a complete metrizable locally convex topological vector space. A sequence {Ln} of continuous linear functional is said to be interpolating if for every sequence {An} of complex numbers, there exists an ƒ ∈ E such that Ln(ƒ) = An for n = 1, 2, 3, … . In this paper, we give necessary and sufficient conditions that {Ln} be an interpolating sequence. They are different from the conditions in [2] and don't seem to be easily interderivable with them.

scholarly journals Solvability of systems of ordinary differential equations in the space of Aronszajn and the determinant over the Weyl algebra

1990 ◽  
Vol 117 ◽  
pp. 207-225 ◽  
Author(s):  
Masatake Miyake
Keyword(s):  
Differential Equations ◽  
Heat Equation ◽  
Ordinary Differential Equations ◽  
Weyl Algebra ◽  
Analytic Solutions ◽  
Fréchet Space ◽  
Frechet Space

N. Aronszajn introduced in [4] an abstract Frechét space R (0<R≤∞), which is isomorphic to the space of analytic solutions of the heat equation in if 0 < R ∞, and in if R = ∞, and called it the space of traces of analytic solutions of the heat equation. Hereafter, we call it the space of traces, shortly.

Local analytic structure in certain commutative topological algebras

1972 ◽  
Vol 6 (2) ◽  
pp. 161-167 ◽  
Author(s):  
R.J. Loy
Keyword(s):  
Power Series ◽  
Topological Algebra ◽  
Fréchet Space ◽  
Analytic Structure ◽  
Frechet Space ◽  
Topological Algebras ◽  
Space Topology ◽  
Formal Power ◽  
Locally Convex Topology ◽  
Locally Convex

Let B be a topological algebra with Fréchet space topology, A an algebra with locally convex topology and an algebra of formal power series over A in n commuting indeterminates which carries a Fréchet space topology. In a previous paper the author showed, for the case n = 1, that a homomorphism of B into whose range contains polynomials is necessarily continuous provided the coordinate projections of into A satisfy a certain equicontinuity condition. This result is here extended to the case of general n, and also to weaker topological assumptions.

On the existence of fixed points in completely continuous operators in F -space

2019 ◽  
pp. 26-32
Author(s):  
Alexander Dorokhov ◽  
Michael Karpov
Keyword(s):  
Fixed Points ◽  
Normed Space ◽  
Fréchet Space ◽  
Frechet Space ◽  
Completely Continuous ◽  
Completely Continuous Operators ◽  
Continuous Operators

This work is dedicated to the development of the theory of fixed points of completely continuous operators. We prove existence of new theorems of fixed points of completely continuous operators in F -space (Frechet space). This class of spaces except Banach includes such important space as a countably normed space and Lp(0 < p < 1), lp(0 < p < 1).

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