2022/08/22 by Aparajita Dasgupta, Dasgupta, Aparajita, Lalit Mohan +3
Computer Science · Mathematics · #35A17 #47G30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Primary 35S05 #Secondary 43A85 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2208.10141
openalex publication_date 2022/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study elements of symbolic calculus for pseudo-differential operators associated with the weighted symbol class Mρ, Λm(\mathbb T× ℤ) (associated to a suitable weight function Λ on ℤ) by deriving formulae for the asymptotic sums, composition, adjoint, transpose. We also construct the parametrix of M-elliptic pseudo-differential operators on \mathbb T. Further, we prove a version of Gohberg's lemma for pseudo-differetial operators with weighted symbol class Mρ, Λ0(\mathbb T× ℤ) and as an application, we provide a sufficient and necessary condition to ensure that the corresponding pseudo-differential operator is compact on L2(\mathbbT). Finally, we provide Gårding's and Sharp Gårding's inequality for M-elliptic operators on ℤ and \mathbbT, respectively, and present an application in the context of strong solution of the pseudo-differential equation Tσ u=f in L2(\mathbbT).