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Extra resources for A formula for the error of finite sinc-interpolation over a finite interval

Sample text

Sup IXnl i xl = } nE~ Lemme. Ii existe un diff4omorphisme Soit ~ @tal4 tun diff4omorDhisme que d r,r' : F(r) ~ F(r') . 0 r4el qui est l'identit4 du voisinage de tel ~(]-r, + r[) = ] - r', + r'[ On suppose -- t Soit x = (x I . . . Posons dr,r,(X Xn) < de F(r) x . , quel que soit X ~V(x) si Nx tel ..... point de que q u e l que s o i t n > Nx ~(xn) .... ) F il existe tun voisinage x' = (x~ . . . x 'n ''" . ) darts de V(x) Ix~ I < ~ " n Donc l'image finie FN par (dr,r, - Id) (engendr4 par lee N x 4tant bijective no,ore fini de ooordonn4es d r,r' de de V x est contenue dans l'espace de dimension premiers veeteurs de base)° x ' x : est bijeetive, d r,r' d r,r' (x) d4pend localement est un diff@omorphisme de classe d'un C°o .

D'apr~s l'unicit6 de la structure f ~io est donc une {M,f}L {M,f} = ~ . pour tousles ~o-application. in- 33 D6monstration de (iii) : Les d6monstrations celles de (i) et (ii) sont exactement les m@mes que utilisant les diff@rentielles des applications au lieu d'utiliser les applications elles-m@mes. Nous en d@duisons imm6diatement Corollaire : I. Quelle que soit la structure de Fredholm @tal6e % sur Si f M ZF Fredholm - compatible avee est tune ~o application de %: M sur M , il existe une structure ZF .

Rant ferm4 et l'application 4tant lo- 39 Corollaire 3- Soit f une application de Fredholm d'indice 6tant munies d'une structure'~/g dans que soit transversale k de M un plongement d'une vari6t6 N . I1 existe une approximation de f n g , ~ dans N' au sens de la N , M et N de dimension finie C1-topologie, tells ~(N' ) o D'apr&s les techniques classiques utilis6es pour les th6or&mes de transversalit6 [11] , il suffit de d6montrer le th6or~me localement Montrons que quel qus soit voisinage Nz pour tout y de Yo darts N' Ig(Y) - ~(Y)I la restriction de Yo E N' ~ < E • ~ W et un voisinage W Soit dans cette carte locale ~ de ID1g(y) - D'~(y)I < ~ f ~ > 0 N' dans et f , il existe uzl N tels que : est transversale .

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A formula for the error of finite sinc-interpolation over a finite interval by Berrut J.


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