Abstract
In this paper we establish a theorem for the generalized Fresnel class F A1,A2 ensuring that various functions are in F A1,A2. We also prove a translation theorem for the analytic Feynman integral of functions in F A1,A2.
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Ahn JM, Johnson GW, Skoug DL (1991) Functions in the Fresnel class of an abstract Wiener space. J Korean Math Soc 28:245–265
Albeverio S, Hoegh-Krohn (1976) Mathematical Theory of Feynman Path Integrals. Lecture Notes in Mathematics, Vol 523. Springer-Verlag, Berlin
Cameron RH, Storvick DA (1982) Some Branch Algebras of Analytic Feynman Integrable Functions. Lecture Notes in Mathematics, Vol 798. Springer-Verlag, Berlin, pp 18–67
Cameron RH, Storvick DA (1982) A new translation theorem for the analytic Feynman integral. Rev Roumaine Math Pures Appl 27:937–944
Chang KS, Johnson GW, Skoug DL (1984) Necessary and sufficient conditions for the Fresnel integrability of certain classes of functions. J Korean Math Soc 21:21–29
Chang KS, Johnson GW, Skoug DL (1987) Functions in the Fresnel class. Proc Amer Math Soc 100:309–318
Chang KS, Johnson GW, Skoug DL (1987) Necessary and sufficient conditions for membership in the Banach algebra S for certain classes of functions. Supplemento ai Rendiconti del Circolo Matematico di Palermo 17:153–171
Feynman RP (1948) Space-time approach to non-relativistic quantum mechanics. Rev Mod Phys 20:367–387
Johnson GW (1984) An unsymmetric Fubini theorem. Amer Math Monthly 91:131–133
Kallianpur G (1970) The role of reproducing kernel Hilbert spaces in the study of Gaussian processes. Adv in Prob 2:49–83 (edited by Ney P), New York
Kallianpur G, Bromley C (1984) Generalized Feynman integrals using analytic continuation in several complex variables. Stochastic Anal Appl 433–450 (edited by Pinsky MA), New York
Kallianpur G, Kannan D, Karandikar RL (1985) Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces and a Cameron-Martin formula. Ann Inst Henri Poincaré 21:323–361
Kuo HH (1975) Gaussian Measures in Banach Spaces. Lecture Notes in Mathematics, Vol 463. Springer-Verlag, Berlin
Yoo I, Chang KS (1993) Notes on analytic Feynman integrable functional. Rocky Mountain J Math 23:1133–1142
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This research was supported in part by the Basic Science Research Program, Ministry of Education.
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Yoo, I. Notes on a generalized Fresnel class. Appl Math Optim 30, 225–233 (1994). https://doi.org/10.1007/BF01183012
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DOI: https://doi.org/10.1007/BF01183012