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2021•Journal of Physics Conference SeriesOpen access

The Fourier Transform and its application in solving the equation

Hanwen Guan, Haoyi Song, Yukun Yang, Jiayuan Zhang

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Abstract

Abstract Fourier transform is a linear transform that applicants in the field of engineering and physics. In this research study, we summarize the fundamental properties of the Fourier transform and its application in solving the wave equation. First, we review the definition of Fourier transform and its inverse form. Then, we show Schwartz space is the invariant subspace of the Fourier transform. We also prove the Plancherel theorem. At last, we apply the Fourier transform to solve the wave equation.

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Abstract Fourier transform is a linear transform that applicants in the field of engineering and physics. In this research study, we summarize the fundamental properties of the Fourier transform and its application in solving the wave equation. First, we review the definition of Fourier transform and its inverse form. Then, we show Schwartz space is the invariant subspace of the Fourier transform. We also prove the Plancherel theorem. At last, we apply the Fourier transform to solve the wave equation.

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Available abstract

Abstract Fourier transform is a linear transform that applicants in the field of engineering and physics. In this research study, we summarize the fundamental properties of the Fourier transform and its application in solving the wave equation. First, we review the definition of Fourier transform and its inverse form. Then, we show Schwartz space is the invariant subspace of the Fourier transform. We also prove the Plancherel theorem. At last, we apply the Fourier transform to solve the wave equation.

Key concepts: Fourier transform on finite groups, Fourier transform, Fractional Fourier transform, Fourier inversion theorem, Hartley transform, Discrete Fourier transform (general), Mathematics, Mathematical analysis

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