In this paper we report on recent results and applications of the so-called SG calculus, focusing, in particular, on its elliptic elements. The topics we discuss include propagation of singularities of (global versions) of wave-front sets, global regularity of solutions to linear and nonlinear partial differential equations on R^d in appropriate function and distribution spaces, and spectral asymtptotics of elliptic, selfadjoint, positive operators on R^d.
Ellipticity in the SG calculus
CORIASCO, Sandro;RODINO, Luigi Giacomo
2015-01-01
Abstract
In this paper we report on recent results and applications of the so-called SG calculus, focusing, in particular, on its elliptic elements. The topics we discuss include propagation of singularities of (global versions) of wave-front sets, global regularity of solutions to linear and nonlinear partial differential equations on R^d in appropriate function and distribution spaces, and spectral asymtptotics of elliptic, selfadjoint, positive operators on R^d.
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