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Definition of Inner product for a function

函数的内积是一种函数之间的二元运算。在复数域\(\mathbb{C}\)中,给定两个复数函数\(f(x), g(x)\),则函数的内积定义为:

\(\displaystyle\left\langle f(x), g(x)\right\rangle_{w(x),x\in(a,b)}:=\int^{x=b}_{x=a}f^{*}(x)g(x)w(x)dx\)

其中,\(w(x)\)是权重函数(weight function),\((a,b)\)是函数内积的定义域,\(f^{*}(x)\)是函数\(f(x)\)的复数共轭
- 权重函数一般是1

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