A topological space X is said to be generated by an ideal I if for all A ⊆ X and all x ∈ A there is E ⊆ A in I such that x ∈ E, and is said to be weakly generated by I if whenever a subset A of X contains E for every E ⊆ A with E ∈ I, then A itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Haus...

A WEAKLY OVER-PENALIZED SYMMETRIC INTERIOR PENALTY METHOD SUSANNE C. BRENNER , LUKE OWENS , AND LI-YENG SUNG Abstract. We introduce a new symmetric interior penalty method for symmetric positive definite second order elliptic boundary value problems, where the jumps across element boundaries are weakly over-penalized. Error estimates are derived in the energy norm and the norm for both conformi...

We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a “semicanonical” fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures on an appropriate bundle. The construction uses elementary features of the representation theory of semisimple real Lie groups, and can be considered a general...

We give a contribution about the study of homogeneous pseudoRiemannian structures on a type of homogeneous spaces, namely, the pseudo-Riemannian generalized symmetric spaces of low dimensions. It is well known that generalized symmetric Riemannian spaces admit homogeneous structures of the class T2 ⊕ T3. The same property holds in the pseudo-Riemannian context. The aim of the present paper is t...