Tomasz Przebinda

Resolution in time-frequency

We introduce a new measure H/sub p/ that is related to the Heisenberg uncertainty principle. The measure predicts the compactness of discrete-time signal descriptions in the sample-frequency phase plane. We conjecture a lower limit on the compaction in the phase plane and show that discretized Gaussians may not provide the most compact basis.

The optimal transform for the discrete Hirschman uncertainty principle

We determine all signals giving equality for the discrete Hirschman uncertainty principle. We single out the case where the entropies of the time signal and its Fourier transform are equal. These signals (up to scalar multiples) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal. The transform may be computed via a fast algorithm due to its relationship to the discrete Fourier transform.

Entropy-based uncertainty measures for L/sup 2/(/spl Ropf//sup n/), /spl lscr//sup 2/(/spl Zopf/), and /spl lscr//sup 2/(/spl Zopf//N/spl Zopf/) with a Hirschman optimal transform for /spl lscr//sup 2/(/spl Zopf//N/spl Zopf/)

A process for the production of a permanently bonded polyester-polyolefin film laminate is disclosed herein. The process involves exposing the surface of polyester or polyolefin film to contact with a flame so as to prime the surface thereof and thereafter coating the primed surface of the film with a layer of a molten polyolefin or polyester, respectively. Flame priming of the polyester or polyolefin film results in a permanent surface modification of the film. Thus, the time lapse between the priming of the polyester or polyolefin film and the subsequent coating with the molten polymer may be a matter of days, if desired. Multi-layer laminates which comprise a substrate-polyester-polyolefin laminate, e.g., paperboard-polyester-polyolefin laminates, can be provided by the process of the present invention by providing a previously formed laminate of a substrate and a polyester film and flame priming the polyester surface of the laminate. Thereafter, a layer of a molten polyolefin is coated onto the primed polyester surface.

On Howe's Duality theorem

Abstract We adopt the Langlands classification to the context of real reductive dual pairs and prove that Howes Duality Correspondence maps hermitian representations to hermitian representations.

Characters, dual pairs, and unipotent representations

Abstract We lift distribution characters of irreducible unitary representations of classical groups from the group to the Lie algebra via the Cayley Transform. Then a specific class of these characters admits Fourier transform supported on the closure of a single nilpotent coadjoint orbit. We calculate also the wave front set of the most singular low rank representations.

Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair.For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true in general.

Analysis in a finite time-frequency plane

We revise our conjecture concerning signals realizing the lower bound on compaction in the phase plane to include a forgotten case of periodization and indicate that this case can be used to develop an orthonormal basis for data lengths N that are the square of an integer.

Local geometry of orbits for an ordinary classical lie supergroup

In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.

A Capelli Harish-Chandra homomorphism

For a real reductive dual pair the Capelli identities define a homomorphism C from the center of the universal enveloping algebra of the larger group to the center of the universal enveloping algebra of the smaller group. In terms of the Harish-Chandra isomorphism, this map involves a ρ-shift. We view a dual pair as a Lie supergroup and offer a construction of the homomorphism C based solely on the Harish-Chandras radial component maps. Thus we provide a geometric interpretation of the ρ-shift.

Holomorphicity of a class of semigroups of measures operating on

In the present paper we consider the class of stable semigroups of measures on a Lie group G. This class contains the Gaussian semigroups. We prove that under certain strongly continuous representations of G acting in LP(G/H), I p < ocx these semigroups are holomorphic and uniformly bounded. Introduction. For a fixed Lie group G, let (S) denote the smallest family of semigroups of measures in G that contains all Gaussian semigroups (i.e., those semigroups whose infinitesimal generators are sub-Laplacians) and is closed with respect to taking sums of generators and subordination. Hulanicki [2] has posed the problem of determining if semigroups in (S) are holomorphic. It is known that Gaussian semigroups are holomorphic [5], but beyond this, additional assumptions are needed. For example, if G is a class two nilpotent group, any semigroup in (S) with L2 densities is holomorphic [3]. In this paper we consider semigroups in the image of (S) under strongly continuous representations of G, and show that, for a certain class of representations, these semigroups are holomorphic. Preliminaries. We identify the Lie algebra of G, q, with left-invariant differential operators by setting d Xf(x) = df(exp tX) It=0 For fixed basis {X1,..., X} of g and multi-index z = (z1. z,) we set I z= z + + +z, and