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Integration of Functions in a Banach Space
National Mathematics Magazine, 1945Vereinfachung der Konstruktion des Birkhoffschen und eines Princeschen Integrals für Funktionen, deren Werte in einem Banachschen Raum liegen.
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Function Spaces and Banach Spaces
1965The theory of integration developed in Chapter Three enables us to define certain spaces of functions that have remarkable properties and are of enormous importance in analysis as well as in its applications. We have already, in § 7, considered spaces whose points are functions. In §7, we considered only the uniform norm ∥ ∥ u [see (7.3)] to define the
Edwin Hewitt, Karl Stromberg
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Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces
2016This paper is a survey on the Hyers–Ulam stability of additive functional inequalities, quadratic functional inequalities, additive ρ-functional inequalities, and quadratic ρ-functional inequalities in Banach spaces and fuzzy Banach spaces. Its content is divided into the following sections: 1. Introduction and Preliminaries.
Choonkil Park +2 more
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Banach Spaces of Continuous Functions
The Annals of Mathematics, 1948If X is any topological space, let B(X) be the space of real bounded continuous functions on X, made into a Banach space by the usual norm II b I = supZExIb(x) 1. According to the Banach-Stone Theorem (see [2], [7], [3],),' if X is compact2 B(X) determines the topology of X, in the sense that if B(X1) is equivalent to B(X2) for compact Xi and X2 then ...
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On local fractal functions in banach spaces
AIP Conference Proceedings, 2015We give a short introduction to local fractal functions defined on several classes of Banach spaces. The emphasis is on the Banach space of bounded functions B, the Lebesgue spaces Lp, 1 ≤ p ≤ ∞, and the Sobolev spaces Wn,p, n ∈ N0and 1 ≤ p ≤ ∞.
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2004
Classical function spaces, such as those of Lebesgue and Sobolev type, have played and continue to play a most important role in Analysis. With the passage of time, questions have naturally arisen which for their complete solution require scales of spaces more finely tuned than these famous predecessors. One of the ways of meeting this need is by means
David E. Edmunds, W. Desmond Evans
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Classical function spaces, such as those of Lebesgue and Sobolev type, have played and continue to play a most important role in Analysis. With the passage of time, questions have naturally arisen which for their complete solution require scales of spaces more finely tuned than these famous predecessors. One of the ways of meeting this need is by means
David E. Edmunds, W. Desmond Evans
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Wavelet Bases in Banach Function Spaces
Bulletin of the Malaysian Mathematical Sciences Society, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Biholomorphic Functions in Dual Banach Spaces
Complex Analysis and Operator Theory, 2011The main result of the paper is Theorem 2.9 stating that a holomorphic self map \(f:G\to G\) is surjective with holomorphic inverse whenever \(G\) is a bounded domain in a separable dual Banach space \(E=X^*\) with the holomorphic separation property (i.e., for all \(x\in\partial G\) there is a holomorphic function \(h_x:U_x\to\mathbb C\) on a ...
Carrión, Humberto +2 more
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