A.2 Fourier transforms

对照

The Fourier transform is defined by

$$\tilde{f}(k)=\frac{1}{\sqrt{2\pi }}{\int }_{-\infty }^{+\infty }f(q)e^{-ikq}dk$$

except for the case of functions of a time variable $t,$ for which we use the opposite sign in the exponent (and a $\hat{\cdot }$ instead of $\tilde{\cdot }$) , i.e.

$$\hat{f}(\omega )=\frac{1}{\sqrt{2\pi }}{\int }_{-\infty }^{+\infty }f(t)e^{i\omega t}d\omega$$

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上一节：A.1 Bilinear forms · 下一节：A.3 Symplectic geometry and quantization

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原书 PDF · 印刷页 534

来源版本：2025-10-20

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