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V Pivovarchik, H. Woracek:
"The square-transform of Hermite-Biehler functions. A geometric approach";
in: "ASC Report 33/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

We investigate the subclass of symmetric indefinite Hermite-Biehler functions
which is obtained from positive definite Hermite-Biehler functions
by means of the square-transform. It is known that functions of this class
can be characterized in terms of the location of their zeros. We give another,
more elementary and geometric, proof of this result. The present
proof employs a `shifting-of-zeros´ perturbation method. We apply our
results to obtain information on the eigenvalues of a concrete boundary
value problems.

Hermite-Biehler class, reproducing kernel Pontryagin space, boundary

http://www.asc.tuwien.ac.at/preprint/2007/asc33x2007.pdf