# Mitja Nedic: Real Quasi-Herglotz functions and B-spline approximation

**Time: **
Wed 2019-06-05 13.15

**Lecturer: **
Mitja Nedic (SU)

**Location: ** Sal 14 (OBS!), SU, kräftriket

Abstract: An admittance passive system can be mathematically modeled by a Herglotz function, i.e. a holomorphic function on the upper half-plane having non-negative imaginary part. The integral representation formula for Herglotz function leads to certain integral identities called sum-rules that are used to derive physical bounds in a variety of technical applications. The integral representation formula can also be utilized in a convex optimization setting to construct an optimal approximating passive realization of a desired target response.

In this talk, we will present an enlargement of the class of Herglotz functions, called (real) quasi-Herglotz functions, that preserves the integral representation formula as well as, in certain cases, the sum-rules. Moreover, we present how the new class of functions can be incorporated into an approximation theory when restricted to functions which are Hölder-continuously extendable to some compact interval of the real line. This turns out to be a formulation that implies that a small subspace of functions whose boundary values are generated by finite B-spline expansions are dense in the larger set of approximants.

This talk is based on joint work with Y. Ivanenko (LnU), M. Gustafsson (LU), B. L. G. Jonsson (KTH), A. Luger (SU) and S. Nordebo (LnU).