Delta operator

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

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

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