Delta operator

In mathematics, a delta operator is a shift-equivariant linear operator $Q\colon\mathbb{K}[x] \longrightarrow \mathbb{K}[x]$ on the vector space of polynomials in a variable $x$ over a field $\mathbb{K}$ that reduces degrees by one.

To say that $Q$ is shift-equivariant means that if $g(x) = f(x + a)$ , then

In other words, if $f$ is a "shift" of $g$ , then $Qf$ is also a shift of $Qg$ , and has the same "shifting vector" $a$ .

单词	Delta operator
释义	Delta operator 英语百科 Delta operator In mathematics, a delta operator is a shift-equivariant linear operator $Q\colon\mathbb{K}[x] \longrightarrow \mathbb{K}[x]$ on the vector space of polynomials in a variable $x$ over a field $\mathbb{K}$ that reduces degrees by one. To say that $Q$ is shift-equivariant means that if $g(x) = f(x + a)$ , then In other words, if $f$ is a "shift" of $g$ , then $Qf$ is also a shift of $Qg$ , and has the same "shifting vector" $a$ .
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