We are delighted to celebrate the successful PhD defense of Arne, who presented his dissertation

Harmonic Analysis on Euclidean Domains with Global Structures

The thesis shows how global structures, such as periodicity from lattices and nonlinear coordinate systems, can be built into Fourier analysis and pseudo-differential tools. It develops inequalities and Sobolev embeddings for fundamental domains, along with a pseudo-differential calculus and PDE results for domains such as cubes, cones, and cylinders. Congratulations, Dr. Arne!

Your work on harmonic analysis has opened new paths, and we are excited to see where your research takes you next. May your future collaborations be fruitful, your ideas continue to inspire, and every new challenge bring you the same joy of discovery. Wishing you all the best in the next chapter of your career!

Supervisors: Prof. Micheal Ruzhansky and Dr. Zhirayr Avetisyan

Examiners: Prof. Mitsuru Sugimoto, Prof. Paula Cerejeiras, Prof. Chun-Yen She, Prof. Zhongkai Tao, Prof. Hans Vernaeve, Dr. Tapendu Rana, Dr. Bolys Sabitbek.

Chair: Prof. Bart De Bruyn