A linear partial differential operator, L, is said to be globally analytic hypoelliptic on some real analytic manifold M without boundary if, for any u ∈ D′(M) such that Lu ∈ C(M), one has u ∈ C(M). It is of some interest to determine under what circumstances this property holds, especially for sums of squares of vector fields satisfying the bracket hypothesis of Hörmander, and for related oper...

In this paper we consider the space-fractional Schr\"odinger equation with a singular potential for wide class of fractional hypoelliptic operators. Such analysis can be conveniently realised in setting graded Lie groups. The is continuation and extension previous one where classical on $\mathbb R^n$ potentials was considered.

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...

Abstract In this paper, we use the representation theory of group $$\textrm{Spin}(m)$$ Spin ( m ) to develop aspects global symbolic calculus pseudo-differential operators on $$\textrm{Spin}(3)$$ 3 and $$\textrm{S...

The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums squares operators, introduced by P. Albano, A. Bove, M. Mughetti, satisfying Hörmander condition which fail to be either locally or microlocally hypoelliptic.

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

We consider certain constant-coefficient differential operators on Rd that have positive-definite symbols. Each such operator Λ with symbol P defines a semigroup of e−tΛ, t>0, admitting continuous convolution kernel HPt for which the large-time behavior HPt(0) cannot be deduced by basic scaling arguments. The simplest example has P(ξ)=(η+ζ2)2+η4, ξ=(η,ζ)∈R2. devise method allows us to determine...