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Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ -function

Nikolai Nikolski (1995)

Annales de l'institut Fourier

It is proved that a subspace of a holomorphic Hilbert space is completely determined by their distances to the reproducing kernels. A simple rule is established to localize common zeros of a subspace of the Hardy space of the unit disc. As an illustration we show a series of discs of the complex plan free of zeros of the Riemann ζ -function.

Dynamics of complex singularities in 1D nonlinear parabolic PDE's

Zoran Grujić (2001)

Studia Mathematica

We establish local-in-time smoothing of a simple model nonlinear parabolic PDE in a scale of weighted Bergman spaces on a strip provided the weights are not too singular. This constitutes a very strong smoothing property since an immediate consequence is that the PDE can "push away" an algebraic-type complex singularity provided that the order of the singularity is small enough.

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