Characterizations of the lebesgue measure and product measures related to holomorphic functions having non-negative imaginary or real part

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http://hdl.handle.net/10138/330901

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Nedic , M 2020 , ' Characterizations of the lebesgue measure and product measures related to holomorphic functions having non-negative imaginary or real part ' , International Journal of Mathematics , vol. 31 , no. 12 , 2050102 . https://doi.org/10.1142/S0129167X20501025

Title: Characterizations of the lebesgue measure and product measures related to holomorphic functions having non-negative imaginary or real part
Author: Nedic, Mitja
Contributor organization: Department of Mathematics and Statistics
Date: 2020-11
Language: eng
Number of pages: 27
Belongs to series: International Journal of Mathematics
ISSN: 0129-167X
DOI: https://doi.org/10.1142/S0129167X20501025
URI: http://hdl.handle.net/10138/330901
Abstract: In this paper, we study a class of Borel measures on Double-struck capital Rn that arises as the class of representing measures of Herglotz-Nevanlinna functions. In particular, we study product measures within this class where products with the Lebesgue measures play a special role. Hence, we give several characterizations of the n-dimensional Lebesgue measure among all such measures and characterize all product measures that appear in this class of measures. Furthermore, analogous results for the class of positive Borel measures on the unit poly-torus with vanishing mixed Fourier coefficients are also presented, and the relation between the two classes of measures with regard to the obtained results is discussed.
Subject: Several complex variables
Herglotz-Nevanlinna functions
Nevanlinna measures
measures with vanishing mixed Fourier coefficients
HERGLOTZ-NEVANLINNA FUNCTIONS
APPROXIMATION
POLYDISK
111 Mathematics
Peer reviewed: Yes
Usage restriction: closedAccess
Self-archived version: submittedVersion


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