We present new results concerning pseudo-differential operators in the function spaces $S^{\mu}_{\nu}(\R^n)$ of Gelfand and Shilov. In particular we discuss $S^{\mu}_{\nu}(\R^n)$-regularity of solutions to SG-elliptic pseudo-differential equations, allowing lower order semilinear perturbations. The results apply to SG-elliptic partial differential equations with polynomial coefficients. We also study the action of Weyl operators and localization operators on $S^{\mu}_{\mu}(\R^n).$
Gelfand-Shilov spaces, pseudo-differential operators and localization operators
CAPPIELLO, Marco;RODINO, Luigi Giacomo
2006-01-01
Abstract
We present new results concerning pseudo-differential operators in the function spaces $S^{\mu}_{\nu}(\R^n)$ of Gelfand and Shilov. In particular we discuss $S^{\mu}_{\nu}(\R^n)$-regularity of solutions to SG-elliptic pseudo-differential equations, allowing lower order semilinear perturbations. The results apply to SG-elliptic partial differential equations with polynomial coefficients. We also study the action of Weyl operators and localization operators on $S^{\mu}_{\mu}(\R^n).$
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