A Continuous Euler Transformation and its Application to Fourier Transforms of Slowly Decaying Functions

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  • Ooura Takuya
    Research Institute of Mathematical Sciences, Kyoto University

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  • 連続Euler変換と減衰の遅い関数のFourier変換への応用
  • レンゾク Euler ヘンカン ト ゲンスイ ノ オソイ カンスウ ノ Fourier ヘンカン エ ノ オウヨウ

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Description

Euler transformation is a linear sequence transformation to accelerate the convergence of alternating series. The series of weights of the transformation is extended to a continuous function which can accelerate Fourier type integrals with slowly convergent integrands. We show that the continuous function can be used to compute Fourier transforms of slowly decaying functions using FFT.

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