Means on dyadic symmetrie sets and polar decompositions

J. Lawson; Y. Lim

doi:10.1007/BF02941530

Means on dyadic symmetrie sets and polar decompositions

J. Lawson
, Y. Lim

Louisiana State University
Kyungpook National University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper we develop the theory of the geometric mean and the spectral mean on dyadic symmetric sets, an algebraic generalization of symmetric spaces of noncompact type, and apply them to obtain decomposition theorems of involutive systems. In particular we show for involutive dyadic symmetric sets: every involutive dyadic symmetric set admits a canonical polar decomposition with factors the geometric and spectral means.

Original language	English
Pages (from-to)	135-150
Number of pages	16
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	74
Issue number	1
DOIs	https://doi.org/10.1007/BF02941530
State	Published - Dec 2004
Externally published	Yes

Keywords

Loop
Mean
Midpoint
Polar decomposition
Spectral mean
Symmetric set
Symmetric space

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10.1007/BF02941530

Cite this

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abstract = "In this paper we develop the theory of the geometric mean and the spectral mean on dyadic symmetric sets, an algebraic generalization of symmetric spaces of noncompact type, and apply them to obtain decomposition theorems of involutive systems. In particular we show for involutive dyadic symmetric sets: every involutive dyadic symmetric set admits a canonical polar decomposition with factors the geometric and spectral means.",

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AU - Lawson, J.

AU - Lim, Y.

PY - 2004/12

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N2 - In this paper we develop the theory of the geometric mean and the spectral mean on dyadic symmetric sets, an algebraic generalization of symmetric spaces of noncompact type, and apply them to obtain decomposition theorems of involutive systems. In particular we show for involutive dyadic symmetric sets: every involutive dyadic symmetric set admits a canonical polar decomposition with factors the geometric and spectral means.

AB - In this paper we develop the theory of the geometric mean and the spectral mean on dyadic symmetric sets, an algebraic generalization of symmetric spaces of noncompact type, and apply them to obtain decomposition theorems of involutive systems. In particular we show for involutive dyadic symmetric sets: every involutive dyadic symmetric set admits a canonical polar decomposition with factors the geometric and spectral means.

KW - Loop

KW - Mean

KW - Midpoint

KW - Polar decomposition

KW - Spectral mean

KW - Symmetric set

KW - Symmetric space

UR - https://www.scopus.com/pages/publications/33646535225

U2 - 10.1007/BF02941530

DO - 10.1007/BF02941530

M3 - Article

AN - SCOPUS:33646535225

SN - 0025-5858

VL - 74

SP - 135

EP - 150

JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

IS - 1

ER -

Means on dyadic symmetrie sets and polar decompositions

Abstract

Keywords

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