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Johnson, G. W.; Skoug, D. L.

A Banach algebra of Feynman integrable functionals with application to an integral equation formally equivalent to Schrödinger’s equation. (English) Zbl 0255.46041

J. Funct. Anal. 12, 129-152 (1973).
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Cited in 1 Review
Cited in 21 Documents

MSC:

46J10 Banach algebras of continuous functions, function algebras
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
46G10 Vector-valued measures and integration
45A05 Linear integral equations
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References:

[1] Beekman, J. A.; Kallman, R. A., Gaussian Markov expectations and related integral equations, Pacific J. Math., 37, 303-318 (1971) · Zbl 0211.20604
[2] Cameron, R. H., The Ilstow and Feynman integrals, J. Anal. Math., 10, 287-361 (1962-1963) · Zbl 0133.07701
[3] Cameron, R. H.; Storvick, D. A., An operator valued function space integral and a related integral equation, J. Math. Mech., 18, 517-552 (1968) · Zbl 0186.20701
[4] Cameron, R. H.; Storvick, D. A., An integral equation related to the Schroedinger equation with an application to integration in function space, (Problems in Analysis (1970), Princeton Univ. Press: Princeton Univ. Press Princeton, New Jersey) · Zbl 0215.19101
[5] Feynman, R. P., Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys., 20, 367-387 (1948) · Zbl 1371.81126
[6] Gelbaum, B. R., Tensor products of Banach algebras, Canad. J. Math., 11, 297-310 (1959) · Zbl 0086.09503
[7] Hille, E.; Phillips, R. S., Functional analysis and semi-groups, (A.M.S. Colloq. Publ., 31 (1957)) · Zbl 0078.10004
[8] Johnson, G. W.; Skoug, D. L., Operator-valued Feynman integrals of certain finite-dimensional functionals, (Proc. Amer. Math. Soc., 24 (1970)), 774-780 · Zbl 0191.40703
[9] Johnson, G. W.; Skoug, D. L., An operator valued function space integral: a sequel to Cameron and Storvick’s paper, (Proc. Amer. Math. Soc., 27 (1971)), 514-519 · Zbl 0208.16503
[10] Johnson, G. W.; Skoug, D. L., Operator-valued Feynman integrals of finite dimensional functionals, Pacific J. Math., 34, 415-425 (1970) · Zbl 0201.46301
[11] G. W. Johnson and D. L. SkougPacific J. Math.; G. W. Johnson and D. L. SkougPacific J. Math. · Zbl 0245.46064
[12] Knopp, K., Theory and applications of infinite series (1947), Hafner: Hafner New York
[13] Naimark, M. A., Normed rings (1964), P. Noordhoff, Ltd: P. Noordhoff, Ltd Groningen, The Netherlands · Zbl 0137.31703
[14] Nelson, E., Operants: A functional calculus for noncommuting operators, (Functional Analysis and Related Fields. Functional Analysis and Related Fields, Proceedings of a conference in honor of Marshall Stone (1970), Springer-Verlag: Springer-Verlag New York) · Zbl 0239.47011
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