Howe's correspondence for a generic harmonic analyst

Howe’s Correspondence for a Generic Harmonic Analyst

The goal of this article is to explain Howe’s correspondence to a reader who is not necessarily an expert on Representation Theory of Real Reductive Groups, but is familiar with general concepts of Harmonic Analysis. We recall Howe’s construction of the Oscillator Representation, the notion of a dual pair and a few basic and general facts concerning the correspondence.

Kobayashi-hitchin Correspondence for Tame Harmonic Bundles and an Application

— We establish the correspondence between tame harmonic bundles and μL-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for μL-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deformed to a variation of polarized Hodge structure. As a consequence, we can conclude ...

Kobayashi-Hitchin correspondence for tame harmonic bundles II

Let X be a smooth projective complex variety with an ample line bundle L, and let D be a simple normal crossing divisor. We establish the Kobayashi-Hitchin correspondence between tame harmonic bundles on X −D and μL-stable parabolic λ-flat bundles with trivial characteristic numbers on (X,D). Especially, we obtain the quasiprojective version of the Corlette-Simpson correspondence between flat b...

Generic polar harmonic transforms for invariant image representation

This paper introduces four classes of rotation-invariant orthogonal moments by generalizing four existing moments that use harmonic functions in their radial kernels. Members of these classes share beneficial properties for image representation and pattern recognition like orthogonality and rotation-invariance. The kernel sets of these generic harmonic function-based moments are complete in the...

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