## Some Selected Research Papers

(as of Jan 2019)

Tyni T and Serov V, *Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line*, Inverse Problems & Imaging **13**:1 (2019), 159-175.

Pohjola V, *Multidimensional Borg-Levinson theorems for unbounded potentials*, Asymptot. Anal. 110, no. 3-4 (2018), 203-226.

Schürmann HW and Serov V, *Parameter dependence and stability of guided TE-waves in a lossless nonlinear dielectric slab structure*, Optics Communications 426 (2018), 110-118.

Serov V and Harju M, *Born approximation for the magnetic Schrödinger operator*, Inverse Problems in Science and Engineering (2018)

Tyni T, *Recovery of singularities from a backscattering Born approximation for a biharmonic operator in 3D*, Inverse Problems **34** (2018), 045007.

Tyni T and Serov V, *Scattering problems for perturbations of the multidimensional biharmonic operator*, Inverse Problems & Imaging **12**:1 (2018), 205-227.

Myllylä T, Harju M, Korhonen V, Bykov A, Kiviniemi V and Meglinsksi I, *Assessment of the dynamics of human glymphatic system by near-infrared spectroscopy*, Journal of Biophotonics (2017)

Pohjola V and Tzou L, *Inverse scattering for the magnetic Schrödinger operator on surfaces with Euclidean ends*, Comm. Math. Phys. 356, 1 (2017), 107-142.

Tyni T and Harju M, *Inverse backscattering problem for perturbations of biharmonic operator*, Inverse Problems **33** (2017), 105002.

Schürmann HW and Serov V, *Theory of TE-polarized waves in a lossless cubic-quintic nonlinear waveguide*, Physical Review A, 93 (2016), 063802.

Serov V, *Borg-Levinson theorem for perturbations of the bi-harmonic operator, *Inverse Problems 32 (2016), 045002*.*

Tyni T, Harju M and Serov V, *Recovery of singularities in a fourth-order operator on the line from limited data*, Inverse Problems **32** (2016), 075001.

Harju M and Serov V, *Three-dimensional direct and inverse scattering for the Schrödinger equation with a general nonlinearity*, Operator Theory: Advances and Applications 236 (2014), Proceedings of 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011.

Fotopoulos G, Harju M and Serov V, *Inverse fixed angle scattering and backscattering for a nonlinear Schroedinger equation in 2D*, Inverse Problems and Imaging 7 (2013), 183-197.

## Lecture Notes

The lecture notes below have been also combined into a single book V. Serov: "Fourier Series and Fourier Transform and Their Applications in Mathematical Physics". It is available from the author and can be found also in Oulu University Library.

Complex analysis, Lecture notes, University of Oulu, 2017.

Operator theory and integral equations, Lecture notes, University of Oulu, 2012

Fourier series and the discrete Fourier transform, Lecture notes, University of Oulu, 2010

Spectral theory of elliptic differential operators, Lecture notes, University of Oulu, 2009

Introduction to partial differential equations, Lecture notes, University of Oulu, 2008

Fourier transform and distributions, Lecture notes, University of Oulu, 2007

Last updated: 4.2.2019