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The stationary phase method with an estimate of the remainder term on a space of large dimension

Published online by Cambridge University Press:  22 January 2016

Daisuke Fujiwara
Daisuke Fujiwara*
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku Tokyo 152, Japan
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In discussing convergence of Feynman path integrals [2], we need a stationary phase method of oscillatory integrals over a space of large dimension. More precisely, we have to know how the remainder term behaves when the dimension of the space goes to ∞ (cf. [2], [3] and [5]). The aim of the present note is to give answer to this question under rather mild assumptions. Application to the Feynman path integrals is discussed in [3] and [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 124 , December 1991 , pp. 61 - 97
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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