Seminario di Geometria e Analisi Complessa
Il Prof. Tao Qian , Universita' di Macau, terra' un seminario dal titolo:
" Phase Derivatives of Nevanlinna Functions with Applications"
Abstract: The study explores a new property of Nevenlinna functions. Writing the non-tangential boundary limit of an inner or outer function in the unit disc into the form $f(e^{it}) = \rho(t)e^{i\theta(t)}; 0 < t<2\pi $; the study concerns the sign-change property of the “phase derivative", that reduces to $\theta’(t)$ if the boundary function has an appropriate parameterization in t. We show through an appropriate formulation that for the inner function case the classical Julia-Wolff-Caratheodory Theorem implies the positive sign- property of the phase derivatives. On the other hand, outer functions do not enjoy such property. This study is motivated by adaptive decomposition of functions into sums of the so called mono-components consisting of boundary values of functions in Hardy spaces with no-negative phase derivatives in their amplitude-phase modulations. It is a generalization of both Fourier series and Fourier transform in the respective contexts. It is the desired representation as it gives change of amplitude and frequency along with change of time, and thus has crucial impacts to the study of signal analysis. The talk is based on a series of recent published work of the speaker and his collaborators.
Il seminario iniziera' alle ore 15.00 precise.