grandes-ecoles 2023 Q22

grandes-ecoles · France · centrale-maths1__official Sequences and Series Properties and Manipulation of Power Series or Formal Series
Let $T$ be a delta endomorphism of $\mathbb{K}[X]$.
For every polynomial $p \in \mathbb{K}[X]$ non-zero, verify that $\deg(Tp) = \deg(p) - 1$. Deduce $\ker(T)$ and the spectrum of $T$.
Let $T$ be a delta endomorphism of $\mathbb{K}[X]$.

For every polynomial $p \in \mathbb{K}[X]$ non-zero, verify that $\deg(Tp) = \deg(p) - 1$. Deduce $\ker(T)$ and the spectrum of $T$.