C∞ functions in infinite dimension and linear partial differential difference equations with constant coefficients
Copyright policy )C∞ functions in infinite dimension and linear partial differential difference equations with constant coefficients
In this paper the authors prove existence and approximation results for solutions of linear partial differential-difference equations with constant coefficients in the space \({\mathbb{E}}(E)\), which is a dense linear subspace of the space of the Silva \(C^{\infty}\)-functions on a nuclear locally convex space E introduced and studied by \textit{J. F. Colombeau} and \textit{S. Ponte} [see ibid. 5, 123-135 (1982)]. Moreover a Hahn-Banach extension theorem for some \(C^{\infty}\)-functions defined on a closed subspace of a DFN space, which is analogous to \textit{P. J. Boland's} result in the holomorphic case [see Trans. Am. Math. Soc. 209, 275-281 (1975; Zbl 0317.46036)], is also obtained.
- University of Santiago de Compostela Spain
- University of Bordeaux France
- University of Bordeaux France
existence and approximation results, Silva \(C^{\infty}\)-functions on a nuclear locally convex space, Locally convex Fréchet spaces and (DF)-spaces, Derivatives of functions in infinite-dimensional spaces, General theory of partial differential operators, DFN space, Hahn-Banach extension theorem, Topological linear spaces of continuous, differentiable or analytic functions, solutions of linear partial differential-difference equations with constant coefficients
existence and approximation results, Silva \(C^{\infty}\)-functions on a nuclear locally convex space, Locally convex Fréchet spaces and (DF)-spaces, Derivatives of functions in infinite-dimensional spaces, General theory of partial differential operators, DFN space, Hahn-Banach extension theorem, Topological linear spaces of continuous, differentiable or analytic functions, solutions of linear partial differential-difference equations with constant coefficients
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!