On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions

LUIS O. SILVA; JULIO H. TOLOZA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2015 vol. 421 p. 996 - 1005

0022-247X

In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined.  First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one perturbations from the viewpoint of the theory of de Branges spaces.  Then, on the basis of the obtained results, we provide new necessary and sufficient conditions for a real, zero-free function to lie in a de Branges space.