Noneuclidean harmonic analysis, the central limit theorem, and long transmission lines with random inhomogeneities
type: Item
instance of: scholarly article
title: Noneuclidean harmonic analysis, the central limit theorem, and long transmission lines with random inhomogeneities
zbMATH Open document ID: 0551.60022
DOI: 10.1016/0047-259X(84)90031-9
published in: Journal of Multivariate Analysis
publication date: 1984-01-01T00:00:00Z
review text: This is an expository paper. The derivation of the ordinary central limit theorem using the Fourier transform on the real line is reviewed. Harmonic analysis on the Poincaré-Lobatchevsky upper half plane H is sketched. This result is then used to solve the heat equation on H, producing a non-Euclidean analogue of the density function for the Gaussian or normal distribution on H. The non-Euclidean central limit theorem for rotation invariant distributions on H with an application to the statistics of long transmission lines is also discussed.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 3878061
zbMATH Keywords: expository paper
zbMATH Keywords: central limit theorem
zbMATH Keywords: rotation invariant distributions
author: Audrey A. Terras
MaRDI profile type: Publication
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full work available at URL: 0047-259x(84)90031-9
OpenAlex ID: W2034997572
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description: scientific article; zbMATH DE number 3878061