2024/10/01 by Fulsche, Robert, van Luijk, Lauritz · 1 citation
#43A99 #47G30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2410.00458
Cordes' characterization of Heisenberg-smooth operators bridges a gap between the theory of pseudo-differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) We can admit general quantization schemes, (2) allow for other phase space geometries, (3) obtain Schatten class analogs of the result, and (4) are able to characterize precisely 'Heisenberg-analytic' operators. For (3), we use QHA to derive Schatten versions of the Calderón-Vaillancourt theorem, which might be of independent interest.