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 language | English |
|---|---|
| Pages (from-to) | 271-295 |
| Number of pages | 25 |
| Journal | Mathematical Physics Analysis and Geometry |
| Volume | 10 |
| Issue number | 4 |
| DOIs | |
| State | Published - Nov 2007 |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)
- Mathematical Physics
- Mathematics(all)
Cite this
Weak convergence and vector-valued functions : Improving the stability theory of Feynman's operational calculi. / Nielsen, Lance.
In: Mathematical Physics Analysis and Geometry, Vol. 10, No. 4, 11.2007, p. 271-295.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Weak convergence and vector-valued functions
T2 - Improving the stability theory of Feynman's operational calculi
AU - Nielsen, Lance
PY - 2007/11
Y1 - 2007/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=43349091211&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=43349091211&partnerID=8YFLogxK
U2 - 10.1007/s11040-007-9033-4
DO - 10.1007/s11040-007-9033-4
M3 - Article
AN - SCOPUS:43349091211
VL - 10
SP - 271
EP - 295
JO - Mathematical Physics Analysis and Geometry
JF - Mathematical Physics Analysis and Geometry
SN - 1385-0172
IS - 4
ER -