36 citations · 83 across the 11 of their papers we have counts for
13 papers
Real rational Herglotz-Nevanlinna functions in two variables and a class of extremals
Ludvig Fagrell, Annemarie Luger
We first revisit the Nevanlinna condition for representing measures of Herglotz-Nevanlinna functions in two variables and give a general operator-theoretic criterion for extremalit…
On eigenvalues of self-adjoint extensions for defect larger than one
Annemarie Luger, Jakob Reiffenstein
Self-adjoint extensions of a symmetric operator are parametrised by Krein's formula, in which the -function interacts with another analytic function (the parameter). We obtain a…
On applications of Herglotz-Nevanlinna functions in material sciences, I: classical theory and applications of sum rules
Annemarie Luger, Miao-Jung Yvonne Ou
This is the first part of the review article which focuses on theory and applications of Herglotz-Nevanlinna functions in material sciences. It starts with the definition of scalar…
On applications of Herglotz-Nevanlinna functions in material sciences, II: extended applications and generalized theory
Miao-Jung Yvonne Ou, Annemarie Luger
Part II of the review article focuses on the applications of Herglotz-Nevanlinna functions in material sciences. It presents a diverse set of applications with details and the role…
On quasi-Herglotz functions in one variable
Annemarie Luger, Mitja Nedic
In this paper, the class of (complex) quasi-Herglotz functions is introduced as the complex vector space generated by the convex cone of ordinary Herglotz functions. We prove chara…
Geometric properties of measures related to holomorphic functions having positive imaginary or real part
Annemarie Luger, Mitja Nedic
In this paper, we study the properties of a certain class of Borel measures on that arise in the integral representation of Herglotz-Nevanlinna functions. In particu…
Quasi-Herglotz functions and convex optimization
Yevhen Ivanenko, Mitja Nedic, Mats Gustafsson +3
We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling of non-passive systems. The linear space of quasi-Herglotz functions…
Passive approximation and optimization using B-splines
Yevhen Ivanenko, Mats Gustafsson, B. L. G. Jonsson +4
A passive approximation problem is formulated where the target function is an arbitrary complex valued continuous function defined on an approximation domain consisting of a finite…
An integral representation for Herglotz-Nevanlinna functions in several variables
Annemarie Luger, Mitja Nedic
In this article, a characterization of the class of Herglotz-Nevanlinna functions in variables is given in terms of an integral representation. Furthermore, alternative conditi…
A characterization of Herglotz-Nevanlinna functions in two variables via integral representations
Annemarie Luger, Mitja Nedic
We derive an integral representation for Herglotz-Nevanlinna functions in two variables which provides a complete characterization of this class in terms of a real number, two non-…
Asymptotics of the Weyl Function for Schrödinger Operators with Measure-Valued Potentials
Annemarie Luger, Gerald Teschl, Tobias Wöhrer
We derive an asymptotic expansion for the Weyl function of a one-dimensional Schrödinger operator which generalizes the classical formula by Atkinson. Moreover, we show that the as…
Characterizations of generalized poles by pole cancellation functions of higher order
Muhamed Borogovac, Annemarie Luger
In this paper the analytic characterization of generalized poles of operator valued generalized Nevanlinna functions (including the length of Jordan chains of the representing rela…
Mark Krein's Method of Directing Functionals and Singular Potentials
Charles Fulton, Heinz Langer, Annemarie Luger
It is shown that M. Krein's method of directing functionals can be used to prove the existence of a scalar spectral measure for certain Sturm-Liouville equations with two singular…