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Zeitschrift für Analysis und ihre Anwendungen

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Volume 1, Issue 1, 1982, pp. 75–82
DOI: 10.4171/ZAA/7

Published online: 1982-02-28

Asymptotische Darstellung verallgemeinerter Fourierintegrale IV

Roland Riedel

The asymptotic behavior of Fourier integrals of the form $$\int^b_a K(t-a) e^{iH(t,s)}dt,$$ where the parameter $s$ tends to a critical point $s_0$, is considered. It is provided that $H(i, s)$ has at $t = a$ a stationary point of (fractional) order $\beta > 0$, and the Fourier transform of the function $K(\tau)$ 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 $K$.

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Riedel Roland: Asymptotische Darstellung verallgemeinerter Fourierintegrale IV. Z. Anal. Anwend. 1 (1982), 75-82. doi: 10.4171/ZAA/7