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Can a sequence of polynomials in a translation invariant linear space (of polynomials, of course) point-wise converge to a polynomial which is not included in that space? In one variable this is impossible.

Can a sequence of polynomials in a translation invariant linear space point-wise converge to a polynomial which is not included in that space? In one variable this is impossible.

Can a sequence of polynomials in a translation invariant linear space (of polynomials, of course) point-wise converge to a polynomial which is not included in that space? In one variable this is impossible.

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Can a sequence of polynomials in a translation invariant linear space pointwise converge to a polynomial which is not included in that space? In one variable this is impossible.

Can a sequence of polynomials in a translation invariant linear space point-wise converge to a polynomial which is not included in that space? In one variable this is impossible.