Entire functions of sine type and their applications

For subharmonic functions that depend only on the real part of $z$, new constructions of “sine type functions” are presented. This term is reserved for entire functions whose deviation from a given function is majorized, everywhere except some collection of disks, by a certain constant. It is shown that the system of exponentials constructed by the zeros of a sine type function for some convex function is complete and minimal in a certain weighted Hilbert space on an interval of the real line.