Overview
In mathematics, a delta operator is a shift-equivariant linear operator on the vector space of polynomials in a variable over a field that reduces degrees by one.
To say that is shift-equivariant means that if , then
In other words, if is a "shift" of , then is also a shift of , and has the same "shifting vector" .
To say that an operator reduces degree by one means that if is a polynomial of degree , then is either a polynomial of degree , or, in case , is 0.
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