Hörmander and magnetic pseudo-differential operators are identified with infinite matrices having strong off-diagonal decay via tight Gabor frames, enabling short proofs of the Calderón-Vaillancourt theorem, Beals commutator criterion, and local trace-class criteria.
H¨ ormander: The Analysis of Linear Partial Differential Operators III: P seudo-Differential Opera- tors
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Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames
Hörmander and magnetic pseudo-differential operators are identified with infinite matrices having strong off-diagonal decay via tight Gabor frames, enabling short proofs of the Calderón-Vaillancourt theorem, Beals commutator criterion, and local trace-class criteria.