Abstract
Via a general construction, we are able to establish a quite general and comprehensive stability theory for Feynman’s operational calculus in the time independent setting. In particular, we are able to establish stability of the operational calculus with respect to general types of the time-ordering measures. While the domain of the operational calculus is somewhat restricted as compared to the “standard” version of the operational calculus (established by Jefferies and Johnson (Russ. J. Math. Phys. 8:153–171, 2001; Mat. Zametki 70:815–838, 2001; Adv. Appl. Clifford Algebras 11:239–264, 2001; Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5:171–199, 2002), the advantages of this relatively minor domain restriction are significant in that the stability theory (with respect to the time-ordering measures) as it stands to this time is contained, essentially in its entirety, in the principle result of this paper, Theorem 2. Moreover, Theorem 2 allows immediate, and rather far-reaching extensions of the stability theory that, until now, have not been possible.
| Original language | English |
|---|---|
| Pages (from-to) | 59-79 |
| Number of pages | 21 |
| Journal | Acta Applicandae Mathematicae |
| Volume | 138 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 10 2014 |
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All Science Journal Classification (ASJC) codes
- Applied Mathematics
Cite this
Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus : The Time Independent Setting. / Nielsen, Lance.
In: Acta Applicandae Mathematicae, Vol. 138, No. 1, 10.07.2014, p. 59-79.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Towards a Comprehensive Stability Theory for Feynman’s Operational Calculus
T2 - The Time Independent Setting
AU - Nielsen, Lance
PY - 2014/7/10
Y1 - 2014/7/10
N2 - Via a general construction, we are able to establish a quite general and comprehensive stability theory for Feynman’s operational calculus in the time independent setting. In particular, we are able to establish stability of the operational calculus with respect to general types of the time-ordering measures. While the domain of the operational calculus is somewhat restricted as compared to the “standard” version of the operational calculus (established by Jefferies and Johnson (Russ. J. Math. Phys. 8:153–171, 2001; Mat. Zametki 70:815–838, 2001; Adv. Appl. Clifford Algebras 11:239–264, 2001; Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5:171–199, 2002), the advantages of this relatively minor domain restriction are significant in that the stability theory (with respect to the time-ordering measures) as it stands to this time is contained, essentially in its entirety, in the principle result of this paper, Theorem 2. Moreover, Theorem 2 allows immediate, and rather far-reaching extensions of the stability theory that, until now, have not been possible.
AB - Via a general construction, we are able to establish a quite general and comprehensive stability theory for Feynman’s operational calculus in the time independent setting. In particular, we are able to establish stability of the operational calculus with respect to general types of the time-ordering measures. While the domain of the operational calculus is somewhat restricted as compared to the “standard” version of the operational calculus (established by Jefferies and Johnson (Russ. J. Math. Phys. 8:153–171, 2001; Mat. Zametki 70:815–838, 2001; Adv. Appl. Clifford Algebras 11:239–264, 2001; Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5:171–199, 2002), the advantages of this relatively minor domain restriction are significant in that the stability theory (with respect to the time-ordering measures) as it stands to this time is contained, essentially in its entirety, in the principle result of this paper, Theorem 2. Moreover, Theorem 2 allows immediate, and rather far-reaching extensions of the stability theory that, until now, have not been possible.
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U2 - 10.1007/s10440-014-9957-1
DO - 10.1007/s10440-014-9957-1
M3 - Article
VL - 138
SP - 59
EP - 79
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
SN - 0167-8019
IS - 1
ER -