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arXiv · 1909.04911

A numerical method of computing oscillatory integral related to hyperfunction theory

Hidenori Ogata
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Abstract

In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is defined by an integral of the Fourier-Laplace transform type, and we obtain the desired integral by the analytic continuation of this analytic function onto the real axis using a continued fraction. We also remark that the proposed method is related to hyperfunction theory, a theory of generalized functions based on complex function theory. Numerical examples show the effectiveness of the proposed method.

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Hidenori Ogata. 2019-09-11. A numerical method of computing oscillatory integral related to hyperfunction theory. https://arxiv.org/abs/1909.04911

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