scholarly journals Moments of vector-valued functions and measures

2009 ◽  
Vol 42 (1) ◽  
pp. 199-210
Author(s):  
Miloslav Duchoň ◽  
Camille Debiève
Keyword(s):  
Banach Space ◽  
Vector Space ◽  
Integrable Function ◽  
Normed Vector Space ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Normed Vector ◽  
Bochner Integrable Function

Abstract There are investigated conditions under which the elements of a normed vector space are the moments of a vector-valued measure, and of a Bochner integrable function, respectively, both with values in a Banach space.

Strict Topologies for Vector-Valued Functions

1974 ◽  
Vol 26 (4) ◽  
pp. 841-853 ◽  
Author(s):  
Robert A. Fontenot
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Measure Theory ◽  
Strict Topology ◽  
Locally Compact ◽  
Topological Measure ◽  
Topological Measure Theory ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space

This paper is motivated by work in two fields, the theory of strict topologies and topological measure theory. In [1], R. C. Buck began the study of the strict topology for the algebra C*(S) of continuous, bounded real-valued functions on a locally compact Hausdorff space S and showed that the topological vector space C*(S) with the strict topology has many of the same topological vector space properties as C0(S), the sup norm algebra of continuous realvalued functions vanishing at infinity. Buck showed that as a class, the algebras C*(S) for S locally compact and C*(X), for X compact, were very much alike. Many papers on the strict topology for C*(S), where S is locally compact, followed Buck's; e.g., see [2; 3].

scholarly journals POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS

2011 ◽  
Vol 84 (1) ◽  
pp. 44-48 ◽  
Author(s):  
MICHAEL G. COWLING ◽  
MICHAEL LEINERT
Keyword(s):  
Banach Space ◽  
Pointwise Convergence ◽  
Function Spaces ◽  
Semigroup Of Operators ◽  
Almost Everywhere ◽  
Vector Valued Function ◽  
Vector Valued Functions ◽  
Complex Valued ◽  
Vector Valued

AbstractA submarkovian C0 semigroup (Tt)t∈ℝ+ acting on the scale of complex-valued functions Lp(X,ℂ) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X,E), when E is a Banach space. It is known that, if f∈Lp(X,ℂ), where 1<p<∞, then Ttf→f pointwise almost everywhere. We show that the same holds when f∈Lp(X,E) .

The M-Space Theory of Tolerances

1990 ◽  
Author(s):  
Joshua U. Turner ◽  
Michael J. Wozny
Keyword(s):  
Vector Space ◽  
Mathematical Theory ◽  
Solid Modeling ◽  
Normed Vector Space ◽  
Space Theory ◽  
Modeling Technology ◽  
Geometric Tolerances ◽  
Normed Vector

Abstract A rigorous mathematical theory of tolerances is an important step toward the automated solution of tolerancing problems. This paper develops a mathematical theory of tolerances in which tolerance specifications are interpreted as constraints on a normed vector space of model variations (M-space). This M-space provides concise representations for both dimensional and geometric tolerances, without deviating from the established tolerancing standards. This paper extends the authors’ previous work to include examples of geometric orientation and form tolerances. We show that the M-space theory supports the development of effective algorithms for the solution of tolerancing problems. Through the use of solid modeling technology, it is possible to automate the solution of such problems.

scholarly journals On the stability of radical septic functional equations

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2229
Author(s):  
Emanuel Guariglia ◽  
Kandhasamy Tamilvanan
Keyword(s):  
Functional Equation ◽  
Approximate Solution ◽  
Vector Space ◽  
Banach Spaces ◽  
Functional Equations ◽  
Normed Vector Space ◽  
Relevant Case ◽  
The Stability ◽  
Normed Vector ◽  
Stability Results

This paper deals with the approximate solution of the following functional equation fx7+y77=f(x)+f(y), where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach spaces and (β,p)-Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case.

scholarly journals The strict topology on a space of vector-valued functions

1979 ◽  
Vol 22 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Liaqat Ali Khan
Keyword(s):  
Scalar Field ◽  
Topological Space ◽  
Vector Space ◽  
Convex Space ◽  
Locally Convex Space ◽  
Strict Topology ◽  
Locally Compact ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex

Let X be a topological space, E a real or complex topological vector space, and C(X, E) the vector space of all bounded continuous E-valued functions on X. The notion of the strict topology on C(X, E) was first introduced by Buck (1) in 1958 in the case of X locally compact and E a locally convex space. In recent years a large number of papers have appeared in the literature concerned with extending the results contained in Buck's paper (1); see, for example, (14), (15), (3), (4), (12), (2), and (6). Most of these investigations have been concerned with generalising the space X and taking E to be the scalar field or a locally convex space.

scholarly journals Two fixed point theorems and invariant integrals

1974 ◽  
Vol 11 (1) ◽  
pp. 15-30 ◽  
Author(s):  
T.J. Cooper ◽  
J.H. Michael
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Fixed Point Theorems ◽  
Normed Vector Space ◽  
Invariant Integrals ◽  
Lower Semi ◽  
Normed Vector

Two fixed point theorems for a subset C of a normed vector space X are established by using the concept of centre. These results differ from previous fixed point theorems in that X is assumed to have a topology T as well as a norm. The norm is required to be lower semi-continuous with respect to T and C is required to be convex, bounded with respect to the norm and compact with respect to T.

Uniform Domains and Uniform Domain Decomposition Property in Real Normed Vector Spaces

2013 ◽  
Vol 113 (1) ◽  
pp. 128 ◽  
Author(s):  
M. Huang ◽  
X. Wang
Keyword(s):  
Vector Space ◽  
Domain Decomposition ◽  
Vector Spaces ◽  
Uniform Domain ◽  
Normed Vector Space ◽  
Decomposition Property ◽  
Uniform Domains ◽  
Normed Vector

Let $E$ be a real normed vector space with $\dim(E)\geq 2$, $D$ a proper subdomain of $E$. In this paper we characterize uniform domains in $E$ in terms of the uniform domain decomposition property. In addition, we discuss the relation between quasiballs and domains with the quasiball decomposition property in $\mathsf{R}^n$.

scholarly journals Abelian ergodic theorems for vector-valued functions

1975 ◽  
Vol 16 (1) ◽  
pp. 57-60 ◽  
Author(s):  
P. E. Kopp
Keyword(s):  
Banach Space ◽  
Ergodic Theorem ◽  
Convergence Theorem ◽  
Direct Application ◽  
Approximation Technique ◽  
Ergodic Theorems ◽  
Resolvent Equation ◽  
Continuous Parameter ◽  
Vector Valued Functions ◽  
Vector Valued

This note contains extensions of the Abelian ergodic theorems in [3] and [6] to functions which take their values in a Banach space. The results are based on an adaptation of Rota's maximal ergodic theorem for Abel limits [8]. Convergence theorems for continuous parameter semigroups are deduced by the approximation technique developed in [3], [6]. A direct application of the resolvent equation also enables us to deduce a convergence theorem for pseudo-resolvents.

scholarly journals Mean value theorems and a Taylor theorem for vector valued functions

1981 ◽  
Vol 24 (1) ◽  
pp. 69-77
Author(s):  
Rudolf Výborný
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Extension Theorem ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex

Two mean value theorems and a Taylor theorem for functions with values in a locally convex topological vector space are proved without the use of the Hahn-Banach extension theorem.

The spectrum and eigenspaces of a meromorphic operator-valued function

1997 ◽  
Vol 127 (5) ◽  
pp. 1027-1051 ◽  
Author(s):  
Robert Magnus
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Spectral Theory ◽  
Approximation Theorem ◽  
Meromorphic Mapping ◽  
Bounded Operators ◽  
Single Operator ◽  
Definition Of ◽  
Vector Valued Functions ◽  
Vector Valued

SynopsisIt is shown how to associate eigenvectors with a meromorphic mapping defined on a Riemann surface with values in the algebra of bounded operators on a Banach space. This generalises the case of classical spectral theory of a single operator. The consequences of the definition of the eigenvectors are examined in detail. A theorem is obtained which asserts the completeness of the eigenvectors whenever the Riemann surface is compact. Two technical tools are discussed in detail: Cauchy-kernels and Runge's Approximation Theorem for vector-valued functions.

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