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        "quote": "然而，这些定义存在一个严重问题。若 $\\varphi$ 是具紧支集的函数，则 ${ \\mathcal { F } } \\varphi$ 一般为整解析函数，因而不可能具有紧支集，因为一个在任何开集上为零的整函数必定处处为零。因此，<a href=\"#equation-12-14\" class=\"cross-reference\" id=\"xref-03-fourier-transforms-2\" data-reference=\"equation-12-14\">式 (12.14)</a> 的右端一般并非良定义。绕过这一困难的一种方法是定义一个更一般的试验函数空间 $S ( \\mathbb { R } )$，称为 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:0af8418c-bf2a-4a4f-9b66-1dc813c55557\" data-concept-route=\"/concept-identities#concept-0af8418c-bf2a-4a4f-9b66-1dc813c55557\" id=\"first-23b30995156bac1fe86b-zh\">快速下降函数(rapidly decreasing function)</u> 空间——即当 $|x|\\to\\infty$ 时趋于 0 的速度快于任何逆幂 $| x | ^ { - n }$ 的函数，",
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