Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
Annales de l'I.H.P. Probabilités et statistiques, Tome 21 (1985) no. 4, pp. 323-361. 
@article{AIHPB_1985__21_4_323_0,
     author = {Kallianpur, G. and Kannan, D. and Karandikar, R. L.},
     title = {Analytic and sequential {Feynman} integrals on abstract {Wiener} and {Hilbert} spaces, and a {Cameron-Martin} formula},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {323--361},
     publisher = {Gauthier-Villars},
     volume = {21},
     number = {4},
     year = {1985},
     mrnumber = {823080},
     zbl = {0583.60049},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1985__21_4_323_0/}
}
TY  - JOUR
AU  - Kallianpur, G.
AU  - Kannan, D.
AU  - Karandikar, R. L.
TI  - Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1985
SP  - 323
EP  - 361
VL  - 21
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1985__21_4_323_0/
LA  - en
ID  - AIHPB_1985__21_4_323_0
ER  - 
%0 Journal Article
%A Kallianpur, G.
%A Kannan, D.
%A Karandikar, R. L.
%T Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1985
%P 323-361
%V 21
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1985__21_4_323_0/
%G en
%F AIHPB_1985__21_4_323_0
Kallianpur, G.; Kannan, D.; Karandikar, R. L. Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula. Annales de l'I.H.P. Probabilités et statistiques, Tome 21 (1985) no. 4, pp. 323-361. http://www.numdam.org/item/AIHPB_1985__21_4_323_0/

[1] S.A. Albeverio and R.J. Høegh-Krohn, Mathematical Theory of Feynman Path Integrals. Lecture Notes in Mathematics, n° 523. Springer-Verlag, Berlin, 1976. | MR | Zbl

[2] R.H. Cameron D.A. Storvick, Some Banach algebras of analytic Feynman integrable functionals. Analytic Functions, Kozubnik, 1979. Lecture Notes in Mathematics, n° 798. Springer-Verlag, Berlin, 1980, p. 18-67. | MR | Zbl

[3] R.H. Cameron and D.A. Storvick, A simple definition of the Feynman integral with applications. Memoirs of the American Mathematical Society, n° 288, 1983. | Zbl

[4] Ph. Combe, R. Rodriguez, G. Rideau and M. Sirugue-Collin, On the cylindrical approximation of the Feynman path integral. Reports on Mathematical Physics, t. 13, 1978, p. 279-294. | Zbl

[5 a] K.D. Elworthy and A. Truman, A Cameron-Martin formula for Feynman integrals. (The origin of Maslov indices). VI International Conference on Mathematical Physics, Berlin, August 1981.

[5 b] K.D. Elworthy and A. Truman, Feynman maps, Cameron-Martin formulas and anharmonic oscillators, Ann. Inst. Henri Poincaré, 1984. | Numdam | Zbl

[6] R.P. Feynman, Space time approach to non-relativistic quantum mechanics. Rev. Mod. Phys., t. 20, 1948, p. 367-387. | MR

[7] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals. McGraw-Hill, New York, 1965. | Zbl

[8] L. Gross, Measurable functions on Hilbert space, Transactions of the Amer. Math. Soc., t. 105, 1962, p. 372-390. | MR | Zbl

[9] K. Ito, Generalized uniform complex measures in the Hibertian metric space with their application to the Feynman integral. Proc. Fifth Berkeley symposium on Mathematical Statistics and Probability, 1967, II, Part 1, p. 145-161. | MR

[10] G.W. Johnson, The equivalence of two approaches to Feynman integral. J. Math. Phys., t. 23, 1982, p. 2090-2096. | MR | Zbl

[11] G. Kallianpur and C. Bromley, Generalized Feynman Integrals Using Analytic Continuation in Several Complex Variables. Stochastic Analysis, M. Pinsky, ed., Marcel-Dekker, 1984. | MR | Zbl

[12] G. Kallianpur, A Cameron-Martin Formula for Feynman Integrals. Tech. Rept. # 13, Center for Stochastic Processes, Dept. of Statistics, Univ. of North Carolina, Chapel Hill, 1982.

[13] H.H. Kuo, Gaussian Measures in Banach Spaces. Lecture Notes in Mathematics, n° 463, Springer, Berlin, 1975. | MR | Zbl

[14] J. Tarski, Feynman type integrals defined in terms of general cylindrical approximations. Feynman Path Integrals, S. Albeverio et al., eds., Lecture Notes in Physics, t. 106, Springer-Verlag, 1979, p. 254-278. | MR

[15] A. Truman, The polygonal path formulation of the Feynman path integrals. Feynman Path Integrals, S. Albeverio et al., eds., Lecture Notes in Physics, t. 106, Springer-Verlag, 1979, p. 73-102. | MR | Zbl

[16] N. Dunford and J.T. Schwartz, Linear Operators. Part II, Interscience Publishers, New York, London, 1963. | MR | Zbl