Analytic signals and harmonic measures

Harmonic and analytic functions on graphs

Harmonic and analytic functions have natural discrete analogues. Harmonic functions can be defined on every graph, while analytic functions (or, more precisely, holomorphic forms) can be defined on graphs embedded in orientable surfaces. Many important properties of the “true” harmonic and analytic functions can be carried over to the discrete setting. We prove that a nonzero analytic function ...

ANALYTIC CONTINUATION IN REPRESENTATIONTHEORY AND HARMONIC ANALYSISbyGestur

| In this paper we discuss topics in harmonic analysis and representation theory related to two diierent real forms G=H and G c =H of a complex semisimple symmetric space G C =H C. We connect representations of G and G c using the theory of involutive representations of semigroups and reeection symmetry. We discuss how to generalize the Segal-Bargmann transform to real forms of bounded symmetri...

The Effect of Length of Pre-task Planning Time on Discourse-analytic Measures and Analytic Ratings in L2 Written Narratives

The favorable gains gleaned from the provision of pre-task planning time (PTP) have struck a chord with SLA researchers as they try to manipulate task features to promote language production and development. In a similar vein, the present study is a two-fold attempt to first compare the effect of the length of pre-task planning time on discourse-analytic measures in narrative written production...

On discrete multiresolution analytic signals

Characterization of analytic phase signals

In many cases, a real-valued signal x(t) may be associated with a complex-valued signal a(t)e ~°(t) , the analytic signal associated with x'(t) with the characteristic properties x(t) = a(t) cos O(t) and "H(a(.)cos0(-))(t) = a(t)sin0(t). Using such obtained amplitude-frequency modulation the instantaneous frequency of x(t) at the time to may be defined to be 0'(t0), provided O'(to) >_ O. The pr...