sala A1-33, godz. 10:30–12:00
Dietmara Vogta (Bergische Universitaet Wuppertal)
Restriction spaces of \(A^\infty\)
Abstract. Let \(A^\infty\) be the space of \(2\pi\) periodic \(C^\infty\)-functions on \(\mathbb{R}\) with vanishing negative Fourier coefficients or, equivalently, the space of holomorphic functions on the unit disc with \(C^\infty\)-boundary values. It is shown that for certain totally disconnected Carleson sets \(E\) the restriction space \(A_\infty (E):=A^\infty|_E\) has a basis, so disproving a claim of S. R. Patel. Among the examples there are the classical Cantor set and sets like \(\{2^{-n}:n=1,2,\ldots\}\cup \{0\}\). To prove our result we show, using a result of Alexander, Taylor and Williams, that in our cases we have \(A_\infty (E)=C_\infty(E)\) where \(C_\infty (E):=C^\infty (\mathbb{R})|_E\). Then we analyze carefully the structure of the restriction spaces \(C_\infty (E)\) making use of analytical tools and of the structure theory of nuclear Fréchet spaces.
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.