Abstract
The semi-group of weighted composition operators (Wn)n≥1 whereWnf(z)=(1+z+…+zn−1)f(zn) on the classical Hardy-Hilbert space H2 of the open unit disk is related to the Riemann Hypothesis (RH) (see [16]). The semigroup (Wn)n≥1 is also closely related to the Invariant Subspace Problem (ISP) and the Periodic Dilation Completeness Problem (PDCP). We obtain results on cyclic vectors, spectra, invariant and reducing subspaces. In particular, we show that several basic questions related to the semigroup (Wn)n≥1 are equivalent to the RH and provide generalizations of the Báez-Duarte criterion for the RH (see [5]).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
