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Iwasawa's Theorem and Integrals on Lie Groups
Author(s) -
Schindler Werner
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931620122
Subject(s) - mathematics , lie group , lebesgue integration , class (philosophy) , decomposition , pure mathematics , product (mathematics) , group (periodic table) , algebra over a field , ecology , chemistry , geometry , organic chemistry , artificial intelligence , computer science , biology
In this paper it is proved that Iwasawa's decomposition transforms a certain class of measures on a Lie group H with finitely many components bijectively into a particular class of product measures. This can be applied to evaluate integrals as well as to construct effective algorithms for stochastic simulations on H. Cases of particular interest are the QR ‐decomposition and the polar decomposition of regular matrices. Moreover, from the latter one can deduce simulation algorithms for specific unbounded Lebesgue densities on ℜ n ( n + 1)/2 .