On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains

Autor:	Princy Thankamani, Nicy Sebastian, Hans J. Haubold
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Dirichlet average generalized type-1 type-2 Dirichlet measures functions of matrix argument Dirichlet measures in the complex domain Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 25, Iss 11, p 1534 (2023)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e25111534
Popis:	This paper is about Dirichlet averages in the matrix-variate case or averages of functions over the Dirichlet measure in the complex domain. The classical power mean contains the harmonic mean, arithmetic mean and geometric mean (Hardy, Littlewood and Polya), which is generalized to the y-mean by de Finetti and hypergeometric mean by Carlson; see the references herein. Carlson’s hypergeometric mean averages a scalar function over a real scalar variable type-1 Dirichlet measure, which is known in the current literature as the Dirichlet average of that function. The idea is examined when there is a type-1 or type-2 Dirichlet density in the complex domain. Averages of several functions are computed in such Dirichlet densities in the complex domain. Dirichlet measures are defined when the matrices are Hermitian positive definite. Some applications are also discussed.
Databáze:	Directory of Open Access Journals
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