Linear fractional transformations of Nevanlinna functions associated with a nonnegative operator - Behrndt, Jussi; Hassi, Seppo; de Snoo, Henk; Wietsma, Rudi; Winkler, Henrik (Birkhäuser, 2013)
In the present paper a subclass of scalar Nevanlinna functions is studied, which coincides with the class of Weyl functions associated to a nonnegative symmetric operator of defect one in a Hilbert space. This class consists of all Nevanlinna functions that are holomorphic on (−∞, 0) and all those Nevanlinna functions that have one negative pole a and are injective on (−∞,a)∪(a,0) . These functions are characterized via integral representations and special attention is paid to linear fractional transformations which arise in extension and spectral problems of symmetric and selfadjoint operators.
Keywords: functional analysis; mathematics; Hilbert space; functions (mathematical methods); operators; complex-valued functions; analytic functions; complex analysis; history; fractions; Matematiikka