grandes-ecoles 2012 QV.E

grandes-ecoles · France · centrale-maths1__psi Differential equations Eigenvalue Problems and Operator-Based DEs
In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$ and $f(t) = \dfrac{\sin t}{t}$ for all $t \in \mathbb{R}^{+*}$, $f$ being extended by continuity at 0.
Deduce from V.D the expression of $(Lf)(x)$ for $x \in E$.
In this part, $\lambda(t) = t$ for all $t \in \mathbb{R}^+$ and $f(t) = \dfrac{\sin t}{t}$ for all $t \in \mathbb{R}^{+*}$, $f$ being extended by continuity at 0.

Deduce from V.D the expression of $(Lf)(x)$ for $x \in E$.