All Questions

Fix a positive even integer $d$ and consider the polynomial $f(x)=c_d x^d+\ldots+c_1x+c_0$, where the $c_i$ are independent random variables that follow the uniform distribution in the interval $[-1,1]...

I am currently facing the following problem: Given a polynomial $f(x) = \sum_{s \in S_f} u_s x^s$, $f(0)\neq 0$, $\lvert S_f \rvert \leq t$ (i.e. $f$ is $t$-sparse) with $u_s$ coming as samples from i....

For $n\in \mathbb{N}$ let $B_n$ be the linear operator taking a function $f$ on the unit interval $I=[0,1]$ to its $n$-th Bernstein polynomial $B_nf$, $$ B_nf(x):=\sum_{k=0}^n\binom{n}{k} f\Big(\...

Let $A = (a_0,a_1,\ldots,a_k)$ be a sequence of strictly positive numbers, and let $A^{\ast k}$ denote the $k$-fold repeated convolution (defined by $A^{\ast 1} = A$ and $A^{\ast k+1} = A^{\ast k} \...

I'm currently involved in a small (but quite time consuming) project where we are trying to get some decent bound for the number $N(P)$ of real zeroes of a random polynomial $P(x)=\sum_{k=0}^n\xi_k x^...