## About me

I am a PhD student in mathematics at Stockholm University since September 2014.

## Teaching

Current:

- Analys B - räkneövningar (VT19)

Previous course responsibilities include Analysis A, Complex analysis and Linear analysis.

## Research

My research centres around complex and functional analysis, mainly Herglotz-Nevanlinna functions, functions of several complex variables and unbounded operators.

Currently, I am focused on studying Herglotz-Nevanlinna functions. These are holomorphic functions mapping the poly-upper half-plane to the closed upper half-plane. In the one variable case, there exist classical integral- and operator-representation results. I am currnelty seeking potentially new results in the multi-dimensional case, which are of particular interest not only in mathematics, but also in engineering and industry.

My current research is part of the project "Complex analysis and convex optimization for EM design" supported by the SSF applied mathematics grant AM13-0011.

My main PhD supervisor is Annemarie Luger, SU. My co-supervisors are Lars Jonsson, KTH and Ragnar Sigurdsson, HI.

### Publications

- "On Herglotz-Nevanlinna functions in several variables" (with A. Luger), J. Math. Anal. Appl. (to appear). DOI: 10.1016/j.jmaa.2018.11.072 (preprints under the title "An integral representation for Herglotz-Nevanlinna functions in several variables": DiVA, arXiv)
- "A characterization of Herglotz-Nevanlinna functions in two variables via integral representations" (with A. Luger), Ark. Mat.,
**55**(1), 2017, 199--216. DOI: 10.4310/ARKIV.2017.v55.n1.a10 (preprint: arXiv)

### Preprints

- "A subclass of bondary measures and the convex-combination problem for Herglotz-Nevanlinna functions in several variables", 2017. arXiv
- "Geometric properties of measures related to to holomorphic functions having positive imaginary or real part" (with A. Luger), 2018. arXiv
- "On pseudo-passive causal operators of slow growth", 2018. arXiv
- "Quasi-Herglotz functions and convex optimization" (with Y. Ivanenko, M. Gustafsson, B. L. G. Jonsson, A. Luger and S. Nordebo), 2018. arXiv

### Other publications

- "Herglotz functions and applications in electromagnetics" (with C. Ehrenborg, Y. Ivanenko, A. Osipov, S. Nordebo, A. Luger, B. L. G. Jonsson, D. Sjöberg and M. Gustafsson), Advances in Mathematical Methods for Electromagnetics, IET 2019 (to appear), edited by K. Kobayashi and P. Smith.
- "Integral representations of Herglotz-Nevanlinna functions", Licentiate thesis at the Department of Mathematics, Stockholm Univerisity, 2017. DiVA
- "On Herglotz-Nevanlinna functions in several variables", Doctoral thesis at the Department of Mathematics, Stockholm Univeristy, 2019. DiVA