β-admissibility of observation operators for hypercontractive semigroups
We prove a Weiss conjecture on (Formula presented.)-admissibility of observation operators for discrete and continuous (Formula presented.)-hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and using a reproducing kernel thesis for Hankel operators. Particular attention is paid to the case (Formula presented.), which corresponds to the unw