Weak convergence and vector-valued functions: Improving the stability theory of Feynman's operational calculi

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Abstract

In this paper we present a theorem that establishes a relation between continuous, norm-bounded functions from a metric space into a separable Hilbert space and weak convergence of sequences of probability measures on the metric space. After establishing this result, it's application to the stability theory of Feynman's operational calculi will be illustrated. We will see that the existing time-dependent stability theory of the operational calculi will be significantly improved when the operator-valued functions take their values in L(H) , H a separable Hilbert space.

Original languageEnglish (US)
Pages (from-to)271-295
Number of pages25
JournalMathematical Physics Analysis and Geometry
Volume10
Issue number4
DOIs
StatePublished - Nov 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Geometry and Topology

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