Tao Qian, University of Macau, Macau Boundary phase
behavior of Blaschke products Abstract It is well known that
the phase derivative of a Möbius transform on the
boundary is, by module a multiple constant, the Poisson kernel. Therefore,
it, in particular, has the positivity property. While finite Blaschke products are trivial, the talk will show that
this positive phase derivative property can be extended to infinite Blaschke products through the Wolff-Julia-Caratheodory theorem in 1930's with the formulation of
non tangential boundary limit. The talk then includes a quick survey on
impacts of this result to signal analysis, especially to DSP (digital signal
processing). The talk finishes with providing information of latest studies
on finding analytic functions with positive boundary phase derivatives. |