The index of transversally elliptic operators on locally homogeneous spaces of finite volume.

Transversally Elliptic Operators

In this paper we investigate the index theory of transversally elliptic pseudo-differential operators in the framework of noncommutative geometry. We give examples of spectral triples in the sense of Alain Connes and Henri Moscovici in [12] that are transversally elliptic but nonelliptic. We prove that these spectral triples satisfy the conditions which ensure the Connes-Moscovici local index f...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

Lattice Action on Finite Volume Homogeneous Spaces

The trace formula for transversally elliptic operators on Riemannian foliations

The main goal of the paper is to generalize the Duistermaat-Guillemin trace formula to the case of transversally elliptic operators on a compact foliated manifold. First, let us recall briefly the setting of the classical formula. Let P be a positive self-adjoint elliptic pseudodifferential operator of order one on a closed manifold M (for example, P = √ ∆, where ∆ is the Laplace-Beltrami opera...