Titchmarsh convolution theorem - Revision history

en>Lgorno: Undid revision 623344593 by Lgorno (talk)

2014-08-29T19:09:33Z

Undid revision 623344593 by Lgorno (talk)

← Older revision		Revision as of 21:09, 29 August 2014
Line 1:		Line 1:
	~~{{Unreferenced\|date=November 2006}}~~		Alyson is what my husband loves to contact me but I don't like when people use my complete title. Office supervising is what she does for a residing. What I adore doing is football but I don't have the time recently. Ohio is exactly where my house is but my spouse wants us to transfer.<br><br>my web page - [http://www.article-galaxy.com/profile.php?a=143251 psychic readers]
	~~In [[mathematics]], the notion of '''alternatization''' or '''alternatisation'''~~ is ~~used~~ to ~~pass from any map to an alternating map~~.

	~~Let <math>S</math> be~~ a ~~set and <math>A</math> an [[abelian group]]~~. ~~Given a map <math>\alpha: S \times S \to A</math>, <math>\alpha</math>~~ is ~~termed an~~ '~~''alternating map''' if <math>\alpha(s,s) = 0</math> for all <math>s \in S</math> and <math>\alpha(s,~~t~~) + \alpha(t,s) = 0</math> for all <math>s,t \in S</math>~~.

	~~The alternatization of a general map <math>\alpha: S \times S \~~to A<~~/math~~> ~~is the map~~ <~~math~~>~~(x,y) \mapsto \alpha(x,y)~~ - ~~\alpha(y,x)<~~/~~math>.~~

	~~The alternatization of an alternating map is simply its double, while the alternatization of a [[symmetric map]] is zero~~.

	~~The alternatization of a [[bilinear map]] is bilinear. There may be non~~-~~bilinear maps whose alternatization is bilinear~~. ~~Most notably, the alternatization of any [[cocycle]] is bilinear~~. ~~This fact plays~~ a ~~crucial role in identifying the second cohomology group of a lattice with the group of alternating bilinear forms on a lattice.~~

	~~[[Category:Algebra]~~]


	~~{{Algebra-stub}}~~
	~~{{Math-stub}}~~

en>Świerczkowski at 08:07, 2 June 2013

2013-06-02T08:07:15Z

← Older revision		Revision as of 10:07, 2 June 2013
Line 1:		Line 1:
	~~Nice to meet you~~, ~~my title~~ is ~~Refugia~~. ~~My day job is~~ a ~~meter reader~~. ~~North Dakota is her beginning place but she will have~~ to ~~transfer 1 day or another. To gather coins~~ is ~~a factor that I~~'~~m completely addicted to.~~<br><br>~~My blog :: [http:~~//~~nuvem~~.tk/~~altergalactica~~/~~MarissaepDonnt std testing at home~~]		{{Unreferenced\|date=November 2006}}
			In [[mathematics]], the notion of '''alternatization''' or '''alternatisation''' is used to pass from any map to an alternating map.

			Let <math>S</math> be a set and <math>A</math> an [[abelian group]]. Given a map <math>\alpha: S \times S \to A</math>, <math>\alpha</math> is termed an '''alternating map''' if <math>\alpha(s,s) = 0</math> for all <math>s \in S</math> and <math>\alpha(s,t) + \alpha(t,s) = 0</math> for all <math>s,t \in S</math>.

			The alternatization of a general map <math>\alpha: S \times S \to A</math> is the map <math>(x,y) \mapsto \alpha(x,y) - \alpha(y,x)</math>.

			The alternatization of an alternating map is simply its double, while the alternatization of a [[symmetric map]] is zero.

			The alternatization of a [[bilinear map]] is bilinear. There may be non-bilinear maps whose alternatization is bilinear. Most notably, the alternatization of any [[cocycle]] is bilinear. This fact plays a crucial role in identifying the second cohomology group of a lattice with the group of alternating bilinear forms on a lattice.

			[[Category:Algebra]]


			{{Algebra-stub}}
			{{Math-stub}}

en>Suslindisambiguator at 20:26, 26 March 2012

2012-03-26T20:26:53Z

New page

Nice to meet you, my title is Refugia. My day job is a meter reader. North Dakota is her beginning place but she will have to transfer 1 day or another. To gather coins is a factor that I'm completely addicted to.<br><br>My blog :: [http://nuvem.tk/altergalactica/MarissaepDonnt std testing at home]