grandes-ecoles 2012 QI.C.2

grandes-ecoles · France · centrale-maths1__mp Sequences and Series Properties and Manipulation of Power Series or Formal Series

Let $k$ be a non-zero natural number. Assume that $g$ is of class $C^{k}$ on $\mathbb{R}$ and that all its derivative functions, up to order $k$, are bounded on $\mathbb{R}$. Show that $f * g$ is of class $C^{k}$ on $\mathbb{R}$ and specify its derivative function of order $k$.

Let $k$ be a non-zero natural number. Assume that $g$ is of class $C^{k}$ on $\mathbb{R}$ and that all its derivative functions, up to order $k$, are bounded on $\mathbb{R}$.\\
Show that $f * g$ is of class $C^{k}$ on $\mathbb{R}$ and specify its derivative function of order $k$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.B.5 QI.C.1 QI.C.2 QI.C.3 QI.D.1 QI.D.2 QI.D.3 QI.D.4 QII.A QII.B.1 QII.B.2 QII.C.1 QII.C.2 QII.C.3 QII.D.1 QII.D.2 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.B.1 QIII.B.2 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5 QIII.C.6 QIII.C.7