Generalized Analytic and Quasi-Analytic Vectors

Quasi-analytic Vectors and Quasi-analytic Functions

Local Gevrey and Quasi - Analytic Hypoellipticity For

Introduction. The db complex is well defined on any smooth CR manifold M, and once a metric is fixed, so is the complex Laplace-Beltrami operator Db on forms of type (p, q). For compact M without boundary, the bb cohomology of M may be studied via Ub [6], and thus local smoothness of solutions to Dbu = ƒ is important. In its own right, Ub is a prototype of doubly characteristic operators. Under...

Generalized Analytic Functions on Generalized Domains

We define the algebra G̃(A) of Colombeau generalized functions on a subset A of the space of generalized points R̃d. If A is an open subset of R̃d, such generalized functions can be identified with pointwise maps from A into the ring of generalized numbers C̃. We study analyticity in G̃(A), where A is an open subset of C̃. In particular, if the domain is an open ball for the sharp norm on C̃, we chara...

Analytic Perturbation of Generalized Inverses

We investigate the analytic perturbation of generalized inverses. Firstly we analyze the analytic perturbation of the Drazin generalized inverse (also known as reduced resolvent in operator theory). Our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent. It allows us to treat regular and singular perturbations in a unified framework. W...

Analytic vectors in continuous p-adic representations

Given a compact p-adic Lie group G over a finite unramified extension L/Qp let GL/Qp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/Qp -representations that coincides with passage to analytic vectors in case L = Qp. On the other hand, we study the functor ”passage to an...