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Remarks on Fujiwara’s stationary phase method on a space of large dimension with a phase function involving electromagnetic fields

Published online by Cambridge University Press:  22 January 2016

Tetsuo Tsuchida
Tetsuo Tsuchida*
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, 920-11 Kanazawa, Japan
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We consider an oscillatory integral of the form

Here each xj, j = 0, 1,…, L, runs in Rd, ν > 1 is a constant and tj, j = 1,…,L, are positive constants. Fujiwara [5] discussed this integral for L large and developed the stationary phase method with an estimate of the remainder term for the phase function S(xL,…, x0) coming from the action integral for a particle in an electric field. But his results cannot be applied to the integral which naturally arises in the discussion of quantum mechanics of a charged particle moving in a magnetic field. In this paper we extend his results to the case for the phase function involving both electric and magnetic fields.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 136 , December 1994 , pp. 157 - 189
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

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