Seminars: T. Bayraktar, Widom factors and extremal polynomials in several complex variables

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) December 18, 2025 12:00, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics) + Zoom

Widom factors and extremal polynomials in several complex variables T. Bayraktar Sabanci University
Abstract: Widom factors quantify the deviation of extremal polynomials (Chebyshev or orthogonal) on a compact set $E \subset \mathbb{C}$ from the exponential growth rate determined by logarithmic capacity. In this talk, I will describe a generalization of Widom factors to compact subsets of $\mathbb{C}^n$. Using tools from pluripotential theory, we define multivariate $L^2$ and sup-norm Widom factors associated with orthogonal polynomials and weighted Chebyshev polynomials, normalized by directional Chebyshev constants and the Monge–Ampère measure. We formulate a multivariate Szegő condition via an exponential relative entropy functional and prove universal lower bounds for these invariants. We also introduce a multivariate Mahler measure relative to a compact set and obtain applications to polynomials with integer coefficients. The talk is based on joint work with Göka̧lp Alpan and Norm Levenberg. Website: https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09