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Stable splittings of Hilbert spaces of functions of infinitely many variables

 
: Griebel, M.; Oswald, P.

:

Journal of complexity 41 (2017), S.126-151
ISSN: 0885-064X
Englisch
Zeitschriftenaufsatz
Fraunhofer SCAI ()

Abstract
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction has been used in an exemplary way for guiding dimension- and scale-adaptive algorithms in application areas such as statistical learning theory, reduced order modeling, and information-based complexity. We prove results on compact embeddings, norm equivalences, and the estimation of ε(lunate)-dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.

: http://publica.fraunhofer.de/dokumente/N-445276.html