This thesis is devoted to the fundamental properties and applications of the Bargmann
transform and the Fock-Segal-Bargmann space. The fundamental properties include unitarity
and invertibility of the transformation in L2 spaces and embeddings of the Fock-Segal-Bargmann spaces in Lp for any p>0. Applications include the linear partial differential
equations such as the time-dependent Schrödinger equation in harmonic potential,
the diffusion equation in self-similar variables, and the linearized Korteweg-de Vries equation, and one nonlinear partial differential equation given by the Gross-Pitaevskii model
for the rotating Bose-Einstein condensate. The main question considered in this work in
the context of linear partial differential equation is whether the envelope of the Gaussian
function remains bounded in the time evolution. We show that the answer to this question
is positive for the diffusion equation, negative for the Schrödinger equation, and unknown
for the Korteweg-de Vries equation. We also address the local and global well-posedness
of the nonlocal evolution equation derived for the Bose-Einstein condensates at the lowest
Landau level. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/26400 |
| Date | January 2021 |
| Creators | Al Asmer, Nabil Abed Allah Ali Jr |
| Contributors | Pelinovsky, Dmitry Jr, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
Page generated in 0.0023 seconds