QLunch: Horia Cornean

Speaker: Horia Cornean

Title: A spectral story related to the classical Euler-Bernoulli polynomial approximation

Abstract: For $\beta>1$ we consider a discrete dynamical system induced by the map $T:[0,1)\to [0,1)$ where $T(x)=\beta x- \lfloor \beta x\rfloor\$. We will investigate some spectral and dynamical properties of its associated (non-selfadjoint) Perron-Frobenius operator. Also, when $\beta\geq 2$ is an integer, we establish an unexpected connection to the classical Euler-Bernoulli approximation formula.