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

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3 Citations (Scopus)

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

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operational calculus
Operational Calculus
metric space
Separable Hilbert Space
Vector-valued Functions
Stability Theory
Hilbert space
Weak Convergence
Metric space
norms
Probability Measure
theorems
Norm
operators
Operator
Theorem

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)
  • Mathematical Physics
  • Mathematics(all)

Cite this

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