I am a Ph.D. student at the Department of Mathematics: Analysis, Logic, and Discrete Mathematics, Ghent University, under the supervision of Professor Michael Ruzhansky. Currently, my main interest is the spectral theory of pseudo-differential operators and its applications to PDE’s. I am also interested in spectral geometry, p-adic analysis and abstract harmonic analysis. In addition to my interest in math, I am also interested in literature. In my spare time, I practice my creative writing and some of my stories have been published by the magazine of the school of literary studies of the Universidad del Valle, among others.
1. Ruzhansky M., Velasquez-Rodriguez J. P., Non-harmonic Gohberg’s lemma, Gershgorin theory and heat equation on manifolds with boundary. https://arxiv.org/abs/1902.00920
2. Velasquez-Rodriguez J. P., Hörmander classes of pseudo-differential operators over the compact group of p-adic integers.https://arxiv.org/abs/1912.11402
3. Velasquez-Rodriguez J. P., Spectral properties of pseudo-differential operators over the compact group of p-adic integers and compact Vilenkin groups. https://arxiv.org/abs/1912.11407
4. Velasquez-Rodriguez J. P., On some spectral properties of pseudo-differential operators on T. Journal of Fourier Analysis and Applications. https://link.springer.com/article/10.1007/s00041-019-09680-2