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        "quote": "对任意函数 $\\varphi ( x )$，其 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:9108ce8e-1818-467c-a25f-8675415492dd\" data-concept-route=\"/concept-identities#concept-9108ce8e-1818-467c-a25f-8675415492dd\" id=\"first-8580ce4b7e4e61afb836-zh\">傅里叶变换(Fourier transform)</u> 是由下式定义的函数 ${ \\mathcal { F } } \\varphi$：",
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        "quote": "\n\n> [!definition] 定义（傅里叶变换）\n> 函数 $\\psi$ 的傅里叶变换记作 $\\mathcal F\\psi$ 或 $\\widetilde\\psi$，其定义为\n>\n> <span id=\"equation-11-3\" class=\"block-anchor\"></span>\n>\n> $$\n> (\\mathcal {F} \\psi) (k) = \\widetilde {\\psi} (k) = \\frac {1}{\\sqrt {2 \\pi}} \\int_ {- \\infty} ^ {\\infty} e ^ {- i k q} \\psi (q) d q\\tag{11.3}\n> $$\n",
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        "quote": "\n\n> [!definition] 定义（闵可夫斯基空间傅里叶变换）\n> 闵可夫斯基空间上函数 $f$ 的[<u class=\"concept-term\" data-concept-reference=\"concepts/analysis/minkowski-space-fourier-transform\" data-concept-identity=\"urn:uuid:9108ce8e-1818-467c-a25f-8675415492dd\" data-concept-route=\"/concept-identities#concept-9108ce8e-1818-467c-a25f-8675415492dd\" id=\"first-3c91f74bd22d187234b0-zh\">傅里叶变换(Fourier transform)</u>](../../../../../concepts/analysis/minkowski-space-fourier-transform)由下式给出\n>\n> $$\n> \\begin{aligned}\n> \\widetilde {f} (p) &= \\frac {1}{(2 \\pi) ^ {2}} \\int_ {M ^ {4}} e ^ {- i p \\cdot x} f (x) d ^ {4} x \\\\[0.45em]\n> &= \\frac {1}{(2 \\pi) ^ {2}} \\int_ {M ^ {4}} e ^ {- i (- p _ {0} x _ {0} + p _ {1} x _ {1} + p _ {2} x _ {2} + p _ {3} x _ {3})} f (x) d x _ {0} d ^ {3} \\mathbf {x}\n> \\end{aligned}\n> $$\n",
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        "quote": "\n\n> [!definition] Definition (Minkowski space Fourier transform)\n> The [<u class=\"concept-term\" data-concept-reference=\"concepts/analysis/minkowski-space-fourier-transform\" data-concept-identity=\"urn:uuid:9108ce8e-1818-467c-a25f-8675415492dd\" data-concept-route=\"/concept-identities#concept-9108ce8e-1818-467c-a25f-8675415492dd\">Fourier transform</u>](../../../../../concepts/analysis/minkowski-space-fourier-transform) of a function $f$ on Minkowski space is given by\n>\n> $$\n> \\begin{aligned}\n> \\widetilde {f} (p) &= \\frac {1}{(2 \\pi) ^ {2}} \\int_ {M ^ {4}} e ^ {- i p \\cdot x} f (x) d ^ {4} x \\\\[0.45em]\n> &= \\frac {1}{(2 \\pi) ^ {2}} \\int_ {M ^ {4}} e ^ {- i (- p _ {0} x _ {0} + p _ {1} x _ {1} + p _ {2} x _ {2} + p _ {3} x _ {3})} f (x) d x _ {0} d ^ {3} \\mathbf {x}\n> \\end{aligned}\n> $$\n",
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