4 problems

Let $f_1$ and $f_2$ be strictly bell-shaped functions, meaning that each derivative $f_i^{(n)}$ changes sign exactly $n$ times and has the corresponding strict zero structure. Supp…

A smooth function $f\colon\mathds{R}\to[0,\infty)$ is bell-shaped if it converges to zero at $\pm\infty$ and, for every $n=0,1,2,\ldots$, its $n$-th derivative changes sign exactly…

Let $f$ be the density function of a positive self-decomposable distribution, with Lévy measure having density $\nu$ on $(0,\infty)$. Suppose that the limit … exists and is greater…

Let $f_k$ be the positive self-decomposable density associated with a non-degenerate non-increasing spectral function $k:(0,+\infty)\to\mathbb{R}^+$, and suppose that $k(0+)>n+1$ f…