An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(R). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant ...

The present paper investigates the behaviour of nonlinear discrete-time dynamics over several steps as a particular case of multi-input dynamics. Introducing for these dynamics a differential representation with jumps, it is shown that the input-to-state or input-to-output behaviours can be represented as suitable compositions of exponential series. Some benefits of these representations are di...

Introduction: Two dimensional unitary transforms play an important role in image processing. The term image transform refers to a class of unitary matrices used for representation of images. In analogy with I-D signals that can be represented by an orthogonal series of basis functions, we can similarly represent an image in terms of a discrete set of basis arrays called “basis images ". These a...

Working at the Lifshitz level, we investigate the van der Waals interactions across a series of layers with a periodic motif. We derive the complete form of the van der Waals interaction as an explicit function of the number of periodic layers. We then compare our result with an approximation based on an anisotropic-continuum representation of the stratified medium. Satisfactory agreement betwe...

For a certain class of locally profinite groups, we show that an irreducible smooth discrete series representation is necessarily supercuspidal and, more strongly, can be obtained by induction from a linear character of a suitable open and compact modulo center subgroup. If F is a non-Archimedean local field, then our class of groups includes the groups of F -points of unipotent algebraic group...

Title of dissertation: DEPENDENCE STRUCTURE IN LEVY PROCESSES AND ITS APPLICATION IN FINANCE Qiwen Chen, Doctor of Philosophy, 2008 Dissertation directed by: Professor Dilip B. Madan Department of Finance In this paper, we introduce DSPMD, discretely sampled process with prespecified marginals and pre-specified dependence, and SRLMD, series representation for Levy process with pre-specified mar...