Nielsen, Lance Feynman’s operational calculus with arbitrary measures: an evolution equation in the general case and examples. (English) Zbl 07529826 Integral Equations Oper. Theory 94, No. 2, Paper No. 15, 87 p. (2022). MSC: 44A99 45D99 46J99 47A56 47A60 47D06 PDF BibTeX XML Cite \textit{L. Nielsen}, Integral Equations Oper. Theory 94, No. 2, Paper No. 15, 87 p. (2022; Zbl 07529826) Full Text: DOI OpenURL
Nielsen, Lance Towards a comprehensive stability theory for Feynman’s operational calculus: the time-dependent setting. (English) Zbl 1382.44005 Acta Appl. Math. 152, No. 1, 1-31 (2017). MSC: 44A40 81Q30 81P40 PDF BibTeX XML Cite \textit{L. Nielsen}, Acta Appl. Math. 152, No. 1, 1--31 (2017; Zbl 1382.44005) Full Text: DOI OpenURL
Johnson, Gerald W.; Lapidus, Michel L.; Nielsen, Lance Feynman’s operational calculus and beyond. Noncommutativity and time-ordering. (English) Zbl 1330.81010 Oxford Mathematical Monographs. Oxford: Oxford University Press (ISBN 978-0-19-870249-8/hbk). xiv, 369 p. (2015). Reviewer: Gert Roepstorff (Aachen) MSC: 81-02 81Q30 81T18 81S40 81Q10 PDF BibTeX XML Cite \textit{G. W. Johnson} et al., Feynman's operational calculus and beyond. Noncommutativity and time-ordering. Oxford: Oxford University Press (2015; Zbl 1330.81010) Full Text: DOI OpenURL
Nielsen, Lance Towards a comprehensive stability theory for Feynman’s operational calculus: the time independent setting. (English) Zbl 1319.81062 Acta Appl. Math. 138, No. 1, 59-79 (2015). MSC: 81S40 47A60 47A25 47N50 PDF BibTeX XML Cite \textit{L. Nielsen}, Acta Appl. Math. 138, No. 1, 59--79 (2015; Zbl 1319.81062) Full Text: DOI OpenURL
Jefferies, Brian Harmonic analysis and stochastic partial differential equations: the stochastic functional calculus. (English) Zbl 1327.47076 Ball, Joseph A. (ed.) et al., Operator theory in harmonic and non-commutative analysis. 23rd international workshop in operator theory and its applications, IWOTA, Sydney, Australia, July 16–20, 2012. Cham: Birkhäuser/Springer (ISBN 978-3-319-06265-5/hbk; 978-3-319-06266-2/ebook). Operator Theory: Advances and Applications 240, 195-220 (2014). MSC: 47N30 60H15 47A60 47D06 47-02 PDF BibTeX XML Cite \textit{B. Jefferies}, Oper. Theory: Adv. Appl. 240, 195--220 (2014; Zbl 1327.47076) Full Text: DOI OpenURL
Nielsen, Lance Weak convergence and Banach space-valued functions: improving the stability theory of Feynman’s operational calculi. (English) Zbl 1246.60011 Math. Phys. Anal. Geom. 14, No. 4, 279-294 (2011). Reviewer: Ilie Valuşescu (Bucureşti) MSC: 60B10 60B12 46B28 47A56 81S99 PDF BibTeX XML Cite \textit{L. Nielsen}, Math. Phys. Anal. Geom. 14, No. 4, 279--294 (2011; Zbl 1246.60011) Full Text: DOI OpenURL
Ahn, Byung Moo Methods for iterative disentangling in Feynman’s operational calculi: the case of time dependent noncommuting operators. (English) Zbl 1295.47007 J. Appl. Math. Inform. 28, No. 3-4, 931-938 (2010). MSC: 47A60 46H30 81R15 PDF BibTeX XML Cite \textit{B. M. Ahn}, J. Appl. Math. Inform. 28, No. 3--4, 931--938 (2010; Zbl 1295.47007) OpenURL
Jefferies, Brian Feynman’s operational calculus and the stochastic functional calculus in Hilbert space. (English) Zbl 1252.47015 Hassell, Andrew (ed.) et al., The AMSI-ANU workshop on spectral theory and harmonic analysis. Proceedings of the workshop, Canberra, Australia, July 13–17, 2009. Canberra: Australian National University, Centre for Mathematics and its Applications (ISBN 978-0-7315-5208-5). Proceedings of the Centre for Mathematics and its Applications, Australian National University 44, 183-210 (2010). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 47A60 47D06 60H15 PDF BibTeX XML Cite \textit{B. Jefferies}, Proc. Cent. Math. Appl. Aust. Natl. Univ. 44, 183--210 (2010; Zbl 1252.47015) OpenURL
Nielsen, Lance Feynman’s operational calculi: using Cauchy’s integral formula. (English) Zbl 1228.32005 New York J. Math. 16, 463-488 (2010). Reviewer: Augustin Mouze (Villeneuve d’Ascq) MSC: 32A26 47A13 47A10 32A05 PDF BibTeX XML Cite \textit{L. Nielsen}, New York J. Math. 16, 463--488 (2010; Zbl 1228.32005) Full Text: EuDML EMIS OpenURL
Nielsen, Lance Feynman’s operational calculi: Disentangling away from the origin. (English) Zbl 1196.47015 Acta Appl. Math. 110, No. 1, 409-429 (2010). Reviewer: Miyeon Kwon (Platteville, WI) MSC: 47A60 44A40 47A13 47N50 81S99 PDF BibTeX XML Cite \textit{L. Nielsen}, Acta Appl. Math. 110, No. 1, 409--429 (2010; Zbl 1196.47015) Full Text: DOI OpenURL
Jefferies, B.; Johnson, G. W. Feynman’s operational calculi: decomposing disentanglings. (English) Zbl 1190.47019 Acta Appl. Math. 109, No. 3, 1131-1154 (2010). MSC: 47A60 46H30 47A25 30G35 PDF BibTeX XML Cite \textit{B. Jefferies} and \textit{G. W. Johnson}, Acta Appl. Math. 109, No. 3, 1131--1154 (2010; Zbl 1190.47019) Full Text: DOI OpenURL
Johnson, Gerald W.; Kim, Byoung Soo Derivational derivatives and Feynman’s operational calculi. (English) Zbl 1185.47005 Houston J. Math. 35, No. 2, 647-664 (2009). Reviewer: Woo Young Lee (Seoul) MSC: 47A13 47A60 47B47 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{B. S. Kim}, Houston J. Math. 35, No. 2, 647--664 (2009; Zbl 1185.47005) Full Text: Link OpenURL
Johnson, Gerald W.; Lapidus, Michel L. Feynman’s operational calculi: auxiliary operations and related disentangling formulas. (English) Zbl 1213.47017 Integr., Math. Theory Appl. 1, No. 1, 21-40 (2008). Reviewer: Claudia-Veronika Meister (Darmstadt) MSC: 47A60 47B48 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{M. L. Lapidus}, Integr., Math. Theory Appl. 1, No. 1, 21--40 (2008; Zbl 1213.47017) OpenURL
Ahn, Byung Moo; Yoo, Il Blending instantaneous and continuous phenomena in Feynman’s operational calculi: The case of time dependent noncommuting operators. (English) Zbl 1168.58301 Commun. Korean Math. Soc. 23, No. 1, 67-80 (2008). MSC: 58D30 47N50 47A60 PDF BibTeX XML Cite \textit{B. M. Ahn} and \textit{I. Yoo}, Commun. Korean Math. Soc. 23, No. 1, 67--80 (2008; Zbl 1168.58301) Full Text: DOI OpenURL
Nielsen, Lance Weak convergence and vector-valued functions: Improving the stability theory of Feynman’s operational calculi. (English) Zbl 1143.47014 Math. Phys. Anal. Geom. 10, No. 4, 271-295 (2007). MSC: 47A60 47A56 28B05 60B10 PDF BibTeX XML Cite \textit{L. Nielsen}, Math. Phys. Anal. Geom. 10, No. 4, 271--295 (2007; Zbl 1143.47014) Full Text: DOI OpenURL
Nielsen, Lance Stability properties for Feynman’s operational calculus in the combined continuous/discrete setting. (English) Zbl 1089.47018 Acta Appl. Math. 88, No. 1, 47-79 (2005). Reviewer: Florian-Horia Vasilescu (Villeneuve d’Ascq) MSC: 47A56 46J15 47A60 60B10 46N50 47N50 PDF BibTeX XML Cite \textit{L. Nielsen}, Acta Appl. Math. 88, No. 1, 47--79 (2005; Zbl 1089.47018) Full Text: DOI OpenURL
Ahn, Byung Moo Extracting linear factors in Feynman’s operational calculi: the case of time dependent noncommuting operators. (English) Zbl 1077.47017 Bull. Korean Math. Soc. 41, No. 3, 573-587 (2004). Reviewer: Kun Soo Chang (Seoul) MSC: 47A60 PDF BibTeX XML Cite \textit{B. M. Ahn}, Bull. Korean Math. Soc. 41, No. 3, 573--587 (2004; Zbl 1077.47017) Full Text: DOI OpenURL
Johnson, G. W.; Kim, B. S. Extracting linear and bilinear factors in Feynman’s operational calculi. (English) Zbl 1051.47013 Math. Phys. Anal. Geom. 6, No. 2, 181-200 (2003). Reviewer: Farruh Mukhamedov (Tashkent) MSC: 47A60 46J15 81Q30 81S99 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{B. S. Kim}, Math. Phys. Anal. Geom. 6, No. 2, 181--200 (2003; Zbl 1051.47013) Full Text: DOI OpenURL
Nielsen, Lance Stability properties of Feynman’s operational calculus for exponential functions of noncommuting operators. (English) Zbl 1041.46053 Acta Appl. Math. 74, No. 3, 265-292 (2002). Reviewer: Joo Sup Chang (Hanyang) MSC: 46T12 58D30 81Q15 46N50 PDF BibTeX XML Cite \textit{L. Nielsen}, Acta Appl. Math. 74, No. 3, 265--292 (2002; Zbl 1041.46053) Full Text: DOI OpenURL
Jefferies, Brian; Johnson, G. W.; Nielsen, Lance Feynman’s operational calculi for time dependent noncommuting operators. (English) Zbl 0984.47013 J. Korean Math. Soc. 38, No. 2, 193-226 (2001). Reviewer: F.H.Vasilescu (Villeneuve d’Ascq) MSC: 47A60 46T12 47N50 28A33 28A25 47A56 46J15 PDF BibTeX XML Cite \textit{B. Jefferies} et al., J. Korean Math. Soc. 38, No. 2, 193--226 (2001; Zbl 0984.47013) OpenURL
Johnson, G. W.; Johnson, Lisa Time maps in the study of Feynman’s operational calculus via Wiener and Feynman path integrals. (English) Zbl 0993.46054 Hida, Takeyuki (ed.) et al., Stochastics in finite and infinite dimensions. Conference in honor of Gopinath Kallianpur, Calcutta, India, December 18-23, 2000. Boston: Birkhäuser. 173-194 (2000). Reviewer: Yuri Kozitsky (Lublin) MSC: 46T12 46G12 28C20 81Q30 81S40 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{L. Johnson}, in: Stochastics in finite and infinite dimensions. Conference in honor of Gopinath Kallianpur, Calcutta, India, December 18--23, 2000. Boston: Birkhäuser. 173--194 (2000; Zbl 0993.46054) OpenURL
Johnson, Gerald W.; Lapidus, Michel L. The Feynman integral and Feynman’s operational calculus. (English) Zbl 0952.46044 Oxford Mathematical Monographs. Oxford: Clarendon Press. xviii, 771 p. (2000). Reviewer: Nicolae Angelescu (Bucureşti) MSC: 46T12 81S40 46-02 46G12 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{M. L. Lapidus}, The Feynman integral and Feynman's operational calculus. Oxford: Clarendon Press (2000; Zbl 0952.46044) OpenURL
Ahn, Byung Moo; Johnson, G. W. Path integrals, Fourier transforms, and Feynman’s operational calculus. (English) Zbl 0981.28011 Appl. Math. Optimization 37, No. 2, 189-203 (1998). MSC: 28C20 42A38 47N50 81S40 PDF BibTeX XML Cite \textit{B. M. Ahn} and \textit{G. W. Johnson}, Appl. Math. Optim. 37, No. 2, 189--203 (1998; Zbl 0981.28011) Full Text: DOI OpenURL
DeFacio, Brian; Johnson, Gerald W.; Lapidus, Michel L. Feynman’s operational calculus and evolution equations. (English) Zbl 0892.47018 Acta Appl. Math. 47, No. 2, 155-211 (1997). MSC: 47A60 81S40 81Q15 47D06 58D30 81U10 81V35 47A55 45A05 PDF BibTeX XML Cite \textit{B. DeFacio} et al., Acta Appl. Math. 47, No. 2, 155--211 (1997; Zbl 0892.47018) Full Text: DOI OpenURL
Lapidus, Michel L. The Feynman integral and Feynman’s operational calculus: A heuristic and mathematical introduction. (English) Zbl 0860.46031 Ann. Math. Blaise Pascal 3, No. 1, 89-102 (1996). MSC: 46G12 81S40 47L10 PDF BibTeX XML Cite \textit{M. L. Lapidus}, Ann. Math. Blaise Pascal 3, No. 1, 89--102 (1996; Zbl 0860.46031) Full Text: DOI Numdam EuDML OpenURL
Kim, Bong Jin Feynman’s operational calculus applied to multiple integrals. (English) Zbl 0944.28012 Commun. Korean Math. Soc. 10, No. 2, 337-348 (1995). MSC: 28C20 46G12 81S40 PDF BibTeX XML Cite \textit{B. J. Kim}, Commun. Korean Math. Soc. 10, No. 2, 337--348 (1995; Zbl 0944.28012) Full Text: DOI OpenURL
DeFacio, B.; Johnson, G. W.; Lapidus, M. L. Feynman’s operational calculus as a generalized path integral. (English) Zbl 0783.60063 Cambanis, Stamatis (ed.) et al., Stochastic processes: a festschrift in honour of Gopinath Kallianpur. New York: Springer-Verlag. 51-60 (1993). MSC: 60H99 60K40 81S40 PDF BibTeX XML Cite \textit{B. DeFacio} et al., in: Stochastic processes: a Festschrift in honour of Gopinath Kallianpur. New York: Springer-Verlag. 51--60 (1993; Zbl 0783.60063) OpenURL
Chang, Joo Sup; Johnson, Gerald W. The Feynman integral and Feynman’s operational calculus: The \({\mathcal L}(L_ 1(\mathbb{R}{}),C_ 0(\mathbb{R}{}))\) theory. (English) Zbl 0736.28006 J. Korean Math. Soc. 28, No. 1, 99-125 (1991). Reviewer: N.Angelescu (Bucureşti) MSC: 28C20 58D30 PDF BibTeX XML Cite \textit{J. S. Chang} and \textit{G. W. Johnson}, J. Korean Math. Soc. 28, No. 1, 99--125 (1991; Zbl 0736.28006) OpenURL
Lapidus, Michel L. Quantification, calcul opérationnel de Feynman axiomatique et intégrale fonctionnelle généralisée. (Quantization, axiomatic Feynman’s operational calculus and generalized functional integral). (French) Zbl 0664.47034 C. R. Acad. Sci., Paris, Sér. I 308, No. 5, 133-138 (1989). MSC: 47D99 81S10 81S40 PDF BibTeX XML Cite \textit{M. L. Lapidus}, C. R. Acad. Sci., Paris, Sér. I 308, No. 5, 133--138 (1989; Zbl 0664.47034) OpenURL
Johnson, G. W.; Lapidus, Michel L. Noncommutative operations on Wiener functionals and Feynman’s operational calculus. (English) Zbl 0663.47016 J. Funct. Anal. 81, No. 1, 74-99 (1988). Reviewer: Y.Kato MSC: 47A60 46H30 81S40 28C20 58D30 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{M. L. Lapidus}, J. Funct. Anal. 81, No. 1, 74--99 (1988; Zbl 0663.47016) Full Text: DOI OpenURL
Lapidus, Michel L. The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman’s operational calculus. (English) Zbl 0626.28008 Stud. Appl. Math. 76, 93-132 (1987). Reviewer: A.Badrikian MSC: 28C20 81Q30 PDF BibTeX XML Cite \textit{M. L. Lapidus}, Stud. Appl. Math. 76, 93--132 (1987; Zbl 0626.28008) Full Text: DOI OpenURL
Johnson, Gerald W.; Lapidus, Michel L. Feynman’s operational calculus, generalized Dyson series and the Feynman integral. (English) Zbl 0621.28010 Operator algebras and mathematical physics, Proc. Summer Conf., Iowa City/Iowa 1985, Contemp. Math. 62, 437-445 (1987). MSC: 28C20 47A55 81Q30 58D30 PDF BibTeX XML OpenURL
Johnson, Gerald W.; Lapidus, Michel L. Une multiplication non commutative des fonctionnelles de Wiener et le calcul opérationnel de Feynman. (A noncommutative multiplication of Wiener functionals and Feynman’s operational calculus). (French) Zbl 0609.46024 C. R. Acad. Sci., Paris, Sér. I 304, 523-526 (1987). MSC: 46G12 28C15 81Q30 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{M. L. Lapidus}, C. R. Acad. Sci., Paris, Sér. I 304, 523--526 (1987; Zbl 0609.46024) OpenURL
Johnson, Gerald W.; Lapidus, Michel L. Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman’s operational calculus. (English) Zbl 0638.28009 Memoirs of the American Mathematical Society 351. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-2413-9; 978-1-4704-0767-4/ebook). 78 p. (1986). Reviewer: A.Badrikian MSC: 28C20 81Q30 81S40 PDF BibTeX XML Cite \textit{G. W. Johnson} and \textit{M. L. Lapidus}, Generalized Dyson series, generalized Feynman diagrams, the Feynman integral and Feynman's operational calculus. Providence, RI: American Mathematical Society (AMS) (1986; Zbl 0638.28009) Full Text: DOI Link OpenURL