MEGHÍVÓ

         We kindly invite you to the Miklós Farkas Seminar.

                  21 February (Thursday) 10.15, BME, H306

Gustaf Söderlind (Lund University, Sweden; guest professor at NUMNET MTA-ELTE reserach group)

Logarithmic norms and Quadratic forms with applications to Calculus of Variations

The logarithmic norm was introduced in 1958 for matrices, and for the purpose of estimating growth rates in initial value problems. Since then, the concept has been extended to nonlinear maps, differential operators and function spaces. There are applications in operator equations in general, including evolution equations as well as boundary value problems. The logarithmic norm is the extremal value of a quadratic form.

In this talk we outline how logarithmic norms of differential operators can be computed, and how they are related to variational calculus and ellipticity. Thus, while one typically seeks the minimizing function in a variational problem, the logarithmic norm is the corresponding extremal value of the functional associated with a particular symmetrized differential operator. There are also connections to eigenvalue problems for selfadjoint and non-selfadjoint operators. This will also be illustrated with an application to classical singular problems, such as the Bessel equation, as well as to the biharmonic operator.