An Improved Remainder Estimate of Stationary Phase Method for Some Oscillatory Integrals over a Space of Large Dimension

• Fujiwara Daisuke

  Gakushuin University

• Kumano-go Naoto

  Kogakuin University

抄録

In discussing time slicing approximations of Feynman's path integrals, one can use stationary phase method for some oscillatory integrals over a space of large dimension. Previously estimates of remainder term of such stationary phase method were given in [2] and [6]. In the present note an improved remainder estimate is given for such stationary phase method. The estimate is sharp enough to give us the second term of semiclassical asymptotic expansion if it is applied to Feynman path integrals of some kind discussed in [6] and [4]. See our forthcoming paper [3].

収録刊行物

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 49 (1), 59-86, 2006

  日本数学会函数方程式論分科会

キーワード

• Stationary phase method
• Fourier integral operators
• Feynman path integral

詳細情報

• CRID: 1390001205112701184
• NII論文ID: 130000140660
• NII論文ID: 30012050072
• DOI: 10.1619/fesi.49.59
• MRID: 2239911
• ISSN: 05328721
• Web Site: http://www.jstage.jst.go.jp/article/fesi/49/1/49_1_59/_pdf
• 本文言語コード: en
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