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			In [[mathematics]], a '''paraproduct''' is a [[non-commutative]] [[bilinear operator]] acting on [[function (mathematics)\|functions]] that in some sense is like the [[product (mathematics)\|product]] of the two functions it acts on. According to [[Svante Janson]] and Jaak Peetre, in an article from 1988,<ref>Svante Janson and Jaak Peetre, [http://www.jstor.org/stable/2000875 "Paracommutators-Boundedness and Schatten-Von Neumann Properties"], ''Transactions of the American Mathematical Society'', Vol. 305, No. 2 (Feb., 1988), pp. 467–504.</ref> "the name 'paraproduct' denotes an idea rather than a unique definition; several versions exist and can be used for the same purposes."

			This said, for a given operator <math>\Lambda</math> to be defined as a paraproduct, it is normally required to satisfy the following properties:
			* It should "reconstruct the product" in the sense that for any pair of functions, <math>(f, g)</math> in its domain,
			:: <math>fg = \Lambda(f, g) + \Lambda(g, f).</math>
			* For any appropriate functions, <math>f</math> and <math>h</math> with <math>h(0)=0</math>, it is the case that <math>h(f) = \Lambda(f, h'(f))</math>.
			* It should satisfy some form of the [[Leibnitz rule]].

			A paraproduct may also be required to satisfy some form of [[Hölder's inequality]].

			==Notes==
			{{Reflist}}

			==Further references==
			* Árpád Bényi, Diego Maldonado, and Virginia Naibo, [http://www.ams.org/notices/201007/rtx100700858p.pdf "What is a Paraproduct?"], ''Notices of the American Mathematical Society'', Vol. 57, No. 7 (Aug., 2010), pp. 858–860.

			[[Category:Bilinear operators]]


			{{algebra-stub}}

en>BattyBot: merged templates into Template:Multiple issues & general fixes using AWB (7961)

2012-03-02T17:34:25Z

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Footwear is huge ability essential items to top off one's outfit. There are few things to say about fashion trend whenever we leave aside shoes or boots. Nowadays, shoes not only protect your feet from cold or obstacle, they play more important role on fashion conscious. For most people, both of them are necessary. If you are searching for one kind of shoes which can make you go in the fashion trend and also comfy to wear in winter, Ugg shoes are the best choice. Blog can be a contraction of 'web record.' Basically, a blog is a log of thoughts, ideas, useful links, photos, videos, ugg news or scandal. Blogs are many posts assembled in chronological order, and many bloggers agree they're type of expression. Blogs, through the late 1990's were lists of links maintained by tech savvy men and women. But, in recent years, blogs have become personal observances, updated regularly, and many accommodate rants and findings. My first suggestion is shopping your boots the net. Usually there some online stores which will give cheaper units. Because sellers online have to compete with so many competitors, they in order to be provide many at affordable prices to attract customers. Just visit the websites, for example, eBay, and type in ugg boots on the inside search box at the top, you can find a list of sellers online who are going to offer real ugg boots with one of the most reasonable bargains. Then what you may need to do next is just comparing and selecting, until you can educate yourself on the most satisfying boots. The obvious solution for this problem would wear your footwear. However, they must halt cheap boots offered with discount stores, otherwise they will wear out quickly and the joint for the sole into the boot proper will be an entrance for merely rocks and burs likewise for dirt and small, unpleasant bugs. Quality boots are winning a hot to guarantee that they won't wear out and let things in through the seams. Redemption Island. As we flash retrace to RI, we see Matt at ease with this isle he has called home for nearly a time. He's endured 2 blindsides and 29 days on RI while only having been in precise game for 7 those days. Tree Mail comes to them, and Mike hopes it's a pizza. Definitely a pizza, though it did tell them that their next Duel would work game's final one. Footwear is amongst the number one products within the internet. This ensures may find your favorite pair online that too with extra fun of discount acquiring. There are various shopping mall clubs on the Internet anyone can join by paying a nominal fee and search the golf iron. With the membership you can usually get a associated with offers and discounts on products sold by them. It's fun shopping through these virtual shops which have most of the product lines sold in regular stores. So become a member and uncover exciting offers and discounts on footwear and buy those cheap UGGs. If you have any concerns relating to exactly where and how to use [http://horizonafrica.com/img/ cheap uggs factory outlet], you can make contact with us at the site.

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