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024 7 $a10.1007/978-3-319-07842-7
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035   $a(EBL)1783084
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035   $a(PQKBTitleCode)TC0001277381
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035   $a(DE-He213)978-3-319-07842-7
035   $a(PPN)179765914
035   $a(MiAaPQ)EBC6235503
035   $a(EXLCZ)993710000000143859
100   $a20140626d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aProbability on compact lie groups /$fby David Applebaum
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (236 p.)
225 1 $aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v70
300   $aIncludes index.
311 08$a1-322-13700-5 
311 08$a3-319-07841-0 
327   $aIntroduction -- 1.Lie Groups -- 2.Representations, Peter-Weyl Theory and Weights -- 3.Analysis on Compact Lie Groups -- 4.Probability Measures on Compact Lie Groups -- 5.Convolution Semigroups of Measures -- 6.Deconvolution Density Estimation -- Appendices -- Index -- Bibliography.
330   $aProbability theory on compact Lie groups deals with the interaction between ?chance? and ?symmetry,? a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
410  0$aProbability Theory and Stochastic Modelling,$x2199-3130 ;$v70
606   $aProbabilities
606   $aHarmonic analysis
606   $aTopological groups
606   $aLie groups
606   $aFunctional analysis
606   $aFourier analysis
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015
606   $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058
615  0$aProbabilities.
615  0$aHarmonic analysis.
615  0$aTopological groups.
615  0$aLie groups.
615  0$aFunctional analysis.
615  0$aFourier analysis.
615 14$aProbability Theory and Stochastic Processes.
615 24$aAbstract Harmonic Analysis.
615 24$aTopological Groups, Lie Groups.
615 24$aFunctional Analysis.
615 24$aFourier Analysis.
676   $a512.55
700   $aApplebaum$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0151518
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910299995703321
996   $aProbability on compact Lie groups$91410403
997   $aUNINA