2018/12/18 by Jörg Seiler, Seiler, Jörg · 1 citation
Mathematics · #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1812.07251
openalex publication_date 2018/12/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Starting out from a new description of a class of parameter-dependent pseudodifferential operators with finite regularity number due to G. Grubb, we introduce a calculus of parameter-dependent, poly-homogeneous symbols whose homogeneous components have a particular type of point-singularity in the covariable-parameter space. Such symbols admit intrinsically a second kind of expansion which is closely related to the expansion in the Grubb-Seeley calculus and permits to recover the resolvent-trace expansion for elliptic pseudodifferential oerators originally proved by Grubb-Seeley. Another application is the invertibility of parameter-dependent operators of Toeplitz type, i.e., operators acting in subspaces determined by zero-order pseudodifferential idempotents.