JournalszaaVol. 1, No. 1pp. 75–82

Asymptotische Darstellung verallgemeinerter Fourierintegrale IV

  • Roland Riedel

    Martin-Luther-Universität Halle-Wittenberg, Germany
Asymptotische Darstellung verallgemeinerter Fourierintegrale IV cover

Abstract

The asymptotic behavior of Fourier integrals of the form

abK(ta)eiH(t,s)dt,\int^b_a K(t-a) e^{iH(t,s)}dt,

where the parameter ss tends to a critical point s0s_0, is considered. It is provided that H(i,s)H(i, s) has at t=at = a a stationary point of (fractional) order β>0\beta > 0, and the Fourier transform of the function K(τ)K(\tau) is given in closed form. Under certain conditions it is demonstrated that it’s possible to obtain an asymptotical expansion of this integral by the Fourier transform of the function KK.

Cite this article

Roland Riedel, Asymptotische Darstellung verallgemeinerter Fourierintegrale IV. Z. Anal. Anwend. 1 (1982), no. 1, pp. 75–82

DOI 10.4171/ZAA/7