sala A1-33, godz. 10:30–12:00
Michaela Langenbrucha (Universitaet Oldenburg)
Taylor coefficient multipliers and interpolation of holomorphic functions
Abstract. This is a report on joint work with P. Domański. I will consider Taylor coefficient multipliers on \(A(R^d)\), that is, continuous linear operators on \(A(R^d)\) such that all monomials are eigenfunctions. The corresponding sequence \((m_\alpha)_{\alpha\in\mathbb{N}^d}\) of eigenvalues is called multiplier sequence. Typical examples of multipliers are Hadamard partial differential operators denoted by \(H(\theta):=\sum_{|\alpha|\leq m}c_\alpha\theta^\alpha\), where \(\theta^\alpha=\prod_{j\leq d}\theta_j^{\alpha_j}\) for \(\theta_j:=x_j\partial/\partial x_j\). I will discuss a characterization of multiplier sequences as interpolating sequence for certain holomorphic functions \(f\), i.e. \(f\) satisfies \(f(\alpha)=m_\alpha\) for any \(\alpha\in \mathbb{N}^d\). This will be used to prove necessary and also sufficient conditions for the surjectivity of multipliers. The evaluation of these conditions is interesting already for Hadamard operators of order 2 in 2 variables.
Odczyt w ramach wspólnego seminarium z Zakładem Analizy Funkcjonalnej UAM. Przed wykładem o godz. 10.00 w klubie profesorskim odbędzie się spotkanie przy kawie i herbacie.