grandes-ecoles 2023 Q42

grandes-ecoles · France · centrale-maths1__official Sequences and Series Properties and Manipulation of Power Series or Formal Series
Let $Q$ be a delta endomorphism with associated polynomial sequence $(q_n)_{n \in \mathbb{N}}$.
Show that there exists a unique invertible endomorphism $T$ such that $$\forall n \in \mathbb{N}, \quad T q_n = \frac{X^n}{n!}$$
Let $Q$ be a delta endomorphism with associated polynomial sequence $(q_n)_{n \in \mathbb{N}}$.

Show that there exists a unique invertible endomorphism $T$ such that
$$\forall n \in \mathbb{N}, \quad T q_n = \frac{X^n}{n!}$$