2015/10/01 by Evanthia Carypis, Carypis, Evanthia, Patrik Wahlberg +1
Mathematics · Physics and Astronomy · #35A18 #35A21 #35Q40 #35Q79 #35S10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.1510.00325
openalex publication_date 2015/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study propagation of phase space singularities for the initial value\nCauchy problem for a class of Schr "odinger equations. The Hamiltonian is the\nWeyl quantization of a quadratic form whose real part is non-negative. The\nequations are studied in the framework of projective Gelfand--Shilov spaces and\ntheir distribution duals. The corresponding notion of singularities is called\nthe Gelfand--Shilov wave front set and means the lack of exponential decay in\nopen cones in phase space. Our main result shows that the propagation is\ndetermined by the singular space of the quadratic form, just as in the\nframework of the Schwartz space, where the notion of singularity is the Gabor\nwave front set.\n