We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of th...

We establish sharp regularity and Fredholm theorems for the ∂̄b-Neumann problem on domains satisfying some non-generic geometric conditions. We use these domains to construct explicit examples of bad behaviour of the Kohn Laplacian: it is not always hypoelliptic up to the boundary, its partial inverse is not compact and it is not globally subelliptic.

We prove that CR lines in an exponentially degenerate boundary are propagators of holomorphic extension. This explains, in the context of the CR geometry, why in this situation the induced Kohn-Laplacian b is not hypoelliptic (Christ [3]). MSC: 32F10, 32F20, 32N15, 32T25

In this paper, we find the asymptotics of integrated density states with remainder estimate for hypoelliptic systems almost periodic (a.p.) coefficients. We use approximate spectral projector method matrix a.p. operators continuous spectrum.