Infinite dimensional oscillatory integrals as projective systems of functionals

Infinite dimensional oscillatory integrals as projective systems of functionals

The theory of infinite dimensional oscillatory integrals and some of its applications are discussed, with special attention to the relations with the original work of K. Itô in this area. A recent general approach to infinite dimensional integration which unifies the case of oscillatory integrals an...

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Veröffentlicht in:Journal of the Mathematical Society of Japan 2015, Vol.67 (4), p.1295-1316
Hauptverfasser: ALBEVERIO, Sergio, MAZZUCCHI, Sonia
Format: Artikel
Sprache:eng
Schlagworte:
28C05
28C20
35C15
35Q41
46M10
60B11
Feynman path integrals
integration theory via linear continuous functionals
measure theory on infinite dimensional spaces
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Zusammenfassung:The theory of infinite dimensional oscillatory integrals and some of its applications are discussed, with special attention to the relations with the original work of K. Itô in this area. A recent general approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented, together with some new developments.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06741295