BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mahishanka Withanachchi (Université Laval) DTSTART:20230209T160000Z DTEND:20230209T164000Z DTSTAMP:20260423T021828Z UID:QARF/6 DESCRIPTION:Title: Pol ynomial approximation in local Dirichlet spaces\nby Mahishanka Withana chchi (Université Laval) as part of Quebec Analysis and Related Fields Gr aduate Seminar\n\n\nAbstract\nThe partial Taylor sums $S_n$\, $n \\geq 0$\ , are finite rank operators on any Banach space of analytic functions on t he open unit disc. In the classical setting of disc algebra\, the precise value of the norm of $S_n$ is not known and thus in the literature they ar e referred as the Lebesgue constants. In this setting\, we just know that they grow like $\\log n$\, modulo a multiplicative constant\, as $n$ tends to infinity. However\, on the weighted Dirichlet spaces $\\D_w$\, we prec isely evaluate the norm of $S_n$. As a matter of fact\, there are differen t ways to put a norm on $\\D_w$. Even though these norms are equivalent\, they lead to different values for the norm of $S_n$\, as an operator on $\ \D_w$. We present three different norms on $\\D_w$\, and in each case we try to obtain the precise value of the operator norm of $S_n$. These resul ts are in sharp contrast to the classical setting of the disc algebra. We also consider the problem for the cesaro means $\\sigma_n$ on local Dirich let spaces and try to find the norm of $\\sigma_n$ precisely for the three different norms that we introduced.\n LOCATION:https://researchseminars.org/talk/QARF/6/ END:VEVENT END:VCALENDAR