### 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 |

### Fingerprint

### 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.

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 -