Schrödinger equations with rough Hamiltonians Article Swipe
Related Concepts
Modulation space
Bounded function
Hamiltonian (control theory)
Mathematics
Class (philosophy)
Nonlinear system
Pure mathematics
Propagator
Pseudodifferential operators
Initial value problem
Mathematical physics
Mathematical analysis
Physics
Quantum mechanics
Computer science
Mathematical optimization
Artificial intelligence
Elena Cordero
,
Fabio Nicola
,
Luigi Rodino
·
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.3934/dcds.2015.35.4805
· OA: W1984136184
YOU?
·
· 2015
· Open Access
·
· DOI: https://doi.org/10.3934/dcds.2015.35.4805
· OA: W1984136184
We consider a class of linear Schr\\"odinger equations in R^d with rough\nHamiltonian, namely with certain derivatives in the Sj\\"ostrand class\n$M^{\\infty,1}$. We prove that the corresponding propagator is bounded on\nmodulation spaces. The present results improve several contributions recently\nappeared in the literature and can be regarded as the evolution counterpart of\nthe fundamental result of Sj\\"ostrand about the boundedness of\npseudodifferential operators with symbols in that class. Finally we consider\nnonlinear perturbations of real-analytic type and we prove local wellposedness\nof the corresponding initial value problem in certain modulation spaces.\n
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