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Feynman maps without improper integrals

Pavel Exner GI Kolerov

TBD mathscidoc:1910.43259

Czechoslovak Journal of Physics B, 31, (11), 1207-1224, 1981.11
The Feynman maps introduced first by Truman are examined. The domain considered here consists of the Fresnel-integrable functions in the sense of Albeverio and Hoegh-Krohn; extensions to wider classes of functions will be studied in the following paper. The original definition of the F-maps is slightly modified: we start from the underlying measures on the Hilbert space of paths in order to avoid use of improper integrals. Some new properties of the F-maps are derived. In particular, the dominated convergence theorem is shown to be not valid for the F<sub>1</sub>-map (or Feynman integral); this fact is of a certain importance for the classical limit of quantum mechanics.
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@inproceedings{pavel1981feynman,
  title={Feynman maps without improper integrals},
  author={Pavel Exner, and GI Kolerov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134945477427788},
  booktitle={Czechoslovak Journal of Physics B},
  volume={31},
  number={11},
  pages={1207-1224},
  year={1981},
}
Pavel Exner, and GI Kolerov. Feynman maps without improper integrals. 1981. Vol. 31. In Czechoslovak Journal of Physics B. pp.1207-1224. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020134945477427788.
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