We prove almost sharp upper bounds for the Lp norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space, as well as their restrictions to maximal flat subspaces. Our proof combines techniques from semiclassical analysis with harmonic theory on reductive groups, and makes use of new asymptotic bounds for spherical functions that are of inde...

We consider a theory of scalar QED on spatially compact $1+1$-dimensional spacetime. By considering constant electric field pointing down the dimension, we compute quantum effective action by integrating out degrees freedom in Euclidean sector. Working saddle-point approximation, uncover two novel branches/physical regimes upon analytically continuing back to real time and discover new result, ...

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

Let (X, d) be a compact metric space, f : X 7→ X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and φ : X 7→ R be a continuous function. We show that the set of points for which the Birkhoff average of φ does not exist (which we call the irregular set) is either empty or has full topol...

This is a brief survey of up-to-date results on holomorphic almost periodic functions and mappings in one and several complex variables, mainly due to the Kharkov mathematical school. While the notion of almost periodic function on R (or R m) seems to be quite understood, it is not the case for holomorphic almost periodic functions on a strip in C (or, more generally, on a tube domain in C m). ...