Sonine formula - Revision history

en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-25T21:52:40Z

References: replace mr template with mr parameter in CS1 templates; using AWB

← Older revision		Revision as of 23:52, 25 September 2014
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	~~In mathematics~~, the '''Denjoy–Koksma inequality''', introduced by {{harvtxt\|Herman\|1979\|loc=p.73}} as a combination of work of [[Arnaud Denjoy]] and the [[Koksma–Hlawka inequality]] of [[Jurjen Ferdinand Koksma]], is a bound for [[Weyl sum]]s <~~math~~>~~\sum_{k=0}^{~~m~~-1}f(x+k\omega)</math> of functions ''f'' of [[bounded variation]]~~.		Hi, everybody! <br>I'm Turkish male :D. <br>I really love Rock stacking!

	~~==Statement==~~

	Suppose that a map ''f'' from the circle ''T'' to itself has irrational rotation number ''α'', and ''p''/''q'' is a rational approximation to ''α'' with ''p'' and ''q'' [[coprime]], \|''α'' – ''p''/''q''\| < 1/''q''<sup>2</sup>. Suppose that ''φ'' is a function of bounded variation, and ''μ'' a [[probability measure]] on the circle invariant under ''f''. Then

	:<~~math~~>~~\left\|\sum_{i=0}^{q-1} \phi f^i(x) - q\int_T \phi \, d\mu \right\| < \operatorname{Var}(\phi)</math>~~
	~~{{harv\|Herman\|1979\|loc=p.73}}~~

	~~==References==~~

	*{{Citation \| last1=Herman \| first1=Michael-Robert \| title=Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations \| url=http://www.numdam.org/item?id=PMIHES_1979__49__5_0 \| mr=538680 \| year=1979 \| journal=[[Publications Mathématiques de l'IHÉS]] \| issn=1618-1913 \| issue=49 \| pages=5–233}}
	*{{Citation \| last1=Kuipers \| first1=L. \| last2=Niederreiter \| first2=H. \| title=Uniform distribution of sequences \| publisher=Wiley-Interscience [John Wiley & Sons] \| location=New York \| isbn=978-0-486-45019-3 \| mr=0419394 \|id= Reprinted by Dover 2006 \| year=1974}}

	~~{{DEFAULTSORT:Denjoy-Koksma inequality}}~~
	~~[[Category:Mathematical analysis]]~~

en>David Eppstein: rm orphan tag

2013-10-13T06:13:19Z

rm orphan tag

← Older revision		Revision as of 08:13, 13 October 2013
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	~~Let me inroduce myself~~, ~~my title~~ is ~~Wade Vue. To gather~~ [~~http:~~/~~/data~~.~~gov.uk/data~~/~~search?~~q~~=marbles marbles] is what she does every week. Debt collecting is her day occupation now. South Carolina is exactly where her home~~ is and ~~she loves every day residing there. If you want to find out more verify out my website: http:~~//~~www~~.~~13abc.com/story/26816881/~~is~~-language-~~of~~-desire-really-worth-your-time-~~and-~~money~~-~~read-my-real-language-of-desire-review-and-find-out~~<~~br>~~<br>~~Here is my website~~ - [http://www.~~13abc~~.~~com~~/~~story/26816881/is-language~~-of-~~desire~~-~~really~~-~~worth~~-~~your~~-~~time~~-~~and-money-read-my-real-language-of-desire-review-and-find-out language of desire reviews~~]		In mathematics, the '''Denjoy–Koksma inequality''', introduced by {{harvtxt\|Herman\|1979\|loc=p.73}} as a combination of work of [[Arnaud Denjoy]] and the [[Koksma–Hlawka inequality]] of [[Jurjen Ferdinand Koksma]], is a bound for [[Weyl sum]]s <math>\sum_{k=0}^{m-1}f(x+k\omega)</math> of functions ''f'' of [[bounded variation]].

			==Statement==

			Suppose that a map ''f'' from the circle ''T'' to itself has irrational rotation number ''α'', and ''p''/''q'' is a rational approximation to ''α'' with ''p'' and ''q'' [[coprime]], \|''α'' – ''p''/''q''\| < 1/''q''<sup>2</sup>. Suppose that ''φ'' is a function of bounded variation, and ''μ'' a [[probability measure]] on the circle invariant under ''f''. Then

			:<math>\left\|\sum_{i=0}^{q-1} \phi f^i(x) - q\int_T \phi \, d\mu \right\| < \operatorname{Var}(\phi)</math>
			{{harv\|Herman\|1979\|loc=p.73}}

			==References==

			*{{Citation \| last1=Herman \| first1=Michael-Robert \| title=Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations \| url=http://www.numdam.org/item?id=PMIHES_1979__49__5_0 \| mr=538680 \| year=1979 \| journal=[[Publications Mathématiques de l'IHÉS]] \| issn=1618-1913 \| issue=49 \| pages=5–233}}
			*{{Citation \| last1=Kuipers \| first1=L. \| last2=Niederreiter \| first2=H. \| title=Uniform distribution of sequences \| publisher=Wiley-Interscience [John Wiley & Sons] \| location=New York \| isbn=978-0-486-45019-3 \| mr=0419394 \|id= Reprinted by Dover 2006 \| year=1974}}

			{{DEFAULTSORT:Denjoy-Koksma inequality}}
			[[Category:Mathematical analysis]]

en>AnomieBOT: Dating maintenance tags: {{Orphan}}

2012-02-09T05:13:57Z

Dating maintenance tags: {{Orphan}}

New page

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