International audienceWe characterize the polynomial decay of orbits of Hilbert space C 0-semigroups in resolvent terms. We also show that results of the same type for general Banach space semigroups and functions obtained recently in Batty and Duyckaerts (J Evol Eq 8:765–780, 2008) are sharp. This settles a conjecture posed in Batty and Duyckaerts (2008)
We obtain a Blaschke-type necessary condition on zeros of analytic functions on the unit disc with different types of exponential growth at the boundary. These conditions are used to prove Lieb-Thirring-type inequalities for the eigenvalues of complex Jacobi matrices.
We obtain sampling and interpolation theorems in weighted spaces of analytic functions for radial weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted Bergman spaces.
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