The operator $(Xf)(x)=-if'(x)$ has Fourier series as eigenfunctions. Which operator $ (Af)(x)=??$ has the Taylor series as its eigenfunctions?

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The operator $$ (Xf)(x)=-if'(x)$$ has fourier series as its eigenfunctions. I was wondering what kind of operator $$ (Af)(x)=??$$ has the taylor series as its eigenfunctions?