An operator valued function space integral: A sequel to Cameron and Storvick's paper
Authors:
G. W. Johnson and D. L. Skoug
Journal:
Proc. Amer. Math. Soc. 27 (1971), 514518
MSC:
Primary 28.46
MathSciNet review:
0272974
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Abstract: Recently Cameron and Storvick introduced and studied an operator valued function space integral related to the Feynman integral. The main theorems of their study establish the existence of the function space integral as a weak operator limit of operators defined at the first stage by finitedimensional integrals. This paper provides a substantial strengthening of their existence theorem giving the function space integrals as strong operator limits rather than as weak operator limits.
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 , An integral equation related to the Schroedinger equation with an application to integration in function space, Bochner Memorial Volume (to appear).
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 E. Hille and R. S. Phillips, Functional analysis and semigroups, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc, Providence, R.I., 1957. MR 19, 664. MR 0089373 (19:664d)
 [5]
 G. W. Johnson and D. L. Skoug, Operatorvalued Feynman integrals of certain finitedimensional functionals. Proc. Amer. Math. Soc. 24 (1970), 774780. MR 0254675 (40:7882)
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 E. Nelson, Feynman integrals and the Schrödinger equation, J. Mathematical Phys. 5 (1964), 332343. MR 28 #4397. MR 0161189 (28:4397)
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 D. L. Skoug and G. W. Johnson, Operatorvalued Feynman integrals of finitedimensional functionals, Pacific J. Math. 34 (1970), 415426. MR 0268728 (42:3625)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197102729745
PII:
S 00029939(1971)02729745
Keywords:
Feynman integral,
Wiener integral,
operator valued function space integral,
Poisson representation,
Bochner integral
Article copyright:
© Copyright 1971 American Mathematical Society
