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Cauchy-de Branges spaces are Hilbert spaces of entire functions defined interms of Cauchy transforms of discrete measures on the plane and generalizingthe classical de Branges theory. We consider extensions of two importantproperties of de Branges spaces to this, more general, setting. First, wediscuss geometric properties (completeness, Riesz bases) of systems ofreproducing kernels corresponding to the zeros of certain entire functionsassociated to the space. In the case of de Branges spaces they correspond toorthogonal bases of reproducing kernels. The second theme of the paper is acharacterization of the density of the domain of multiplication by $z$ inCauchy-de Branges spaces.

Cauchy-de Branges spaces, geometry of their reproducing kernels and multiplication operators