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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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An Exotic Minimal Banach Space of Functions
Mathematische Nachrichten, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feichtinger, Hans Georg +1 more
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A Banach–Zarecki Theorem for functions with values in Banach spaces
Monatshefte für Mathematik, 2014This paper gives a vector valued version of the classical Banach-Zarecki theorem, which establishes that a function \(F:[a,b] \to \mathbb R\) is strongly absolutely continuous if and only if \(F\) is of bounded variation, continuous on \([a,b]\) and satisfies the property (N), that is, for each Lebesgue measurable subset \(E\) of \([a,b]\), its ...
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Weighted Noncommutative Banach Function Spaces
2019We review the concept of a weighted noncommutative Banach function space. This concept constitutes a generalisation of the by now well-known theory of noncommutative Banach function spaces associated with a semifinite von Neumann algebra. In this review we remind the reader of the quantum statistical problem which gave birth to this concept, we ...
Labuschagne, L.E., Steyn, C.
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Semicontinuity of an integral functional in Banach space
Siberian Mathematical Journal, 1997In the paper under review the author studies lower semicontinuity of an integral functional \(J_f :(x, u) \to \int_T f(x(t),u(t))dt\) that arises in various minimization problems. It is assumed that \(T\) equals \([0,1]\) and \(x\), \(u\) are elements in the space \(L_1(T,X)\) of all Bochner integrable functions taking values in a separable Banach ...
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A Function Representation for Learning in Banach Spaces
2004Kernel–based methods are powerful for high dimensional function representation. The theory of such methods rests upon their attractive mathematical properties whose setting is in Hilbert spaces of functions. It is natural to consider what the corresponding circumstances would be in Banach spaces.
Charles A. Micchelli +1 more
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On a minimization of functionals in Banach spaces
1981Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 33 (1979), s. 165-188 ; streszcz. pol., ros. ; Artykuł w: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica. Vol. 33 (1979), s. 165-188 ; streszcz. pol., ros.
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