grandes-ecoles 2012 QI.D.4

grandes-ecoles · France · centrale-maths1__mp Sequences and Series Convergence/Divergence Determination of Numerical Series
Does there exist a function $g \in C_{b}(\mathbb{R})$ such that for every function $f$ in $L^{1}(\mathbb{R})$, we have $f * g = f$? 
Does there exist a function $g \in C_{b}(\mathbb{R})$ such that for every function $f$ in $L^{1}(\mathbb{R})$, we have $f * g = f$?
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