New PDF release: Analyse Mathématique II: Calculus différentiel et intégral,

By Roger Godement

ISBN-10: 3540634142

ISBN-13: 9783540634140

Les deux premiers volumes sont consacrés aux fonctions dans R ou C, y compris los angeles théorie élémentaire des séries et intégrales de Fourier et une partie de celle des fonctions holomorphes. L'exposé non strictement linéaire, mix symptoms historiques et raisonnements rigoureux. Il montre los angeles diversité des voies d'accès aux principaux résultats afin de familiariser le lecteur avec les méthodes de raisonnement et idées fondamentales plutôt qu'avec les strategies de calcul, element de vue utile aussi aux personnes travaillant seules.
Les volumes three et four traitent principalement des fonctions analytiques (théorie de Cauchy, théorie analytique des nombres et fonctions modulaires), ainsi que du calcul différentiel sur les variétés, avec un exposé de l'intégrale de Lebesgue, en suivant d'assez près le célèbre cours donné longtemps par l'auteur à l'Université Paris 7.
On reconnaîtra dans ce nouvel ouvrage le kind inimitable de l'auteur, et pas seulement par son refus de l'écriture condensée en utilization dans ce nombreux manuels.

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Additional info for Analyse Mathématique II: Calculus différentiel et intégral, séries de Fourier, fonctions holomorphes

Sample text

9(X), then (c) a vector space (resp. 2(h), is a vector space (resp. an algebra). In particular, is ax-stable if is ay -stable. (e)d(Taf) = d(Ta(a)fU) dy(a(a)) for any a E X and f E (f) a: (X, p) —* (Y,q) is an [81-extension (cf. 4). e. is a . If = 0(X), then g(Y) = g(a(X)) for any g E 0(Y). Indeed, suppose that a E g(Y) \ g(a(X)). 1 on 1 on X, and therefore, by the identity principle, (g —a). f(Y contradiction. = Jgoallx,g E (h)1f Consequently, "= 3t'°°(Y) and a*: —k ,Y°°(X) is an isometry of Banach algebras.

P(x), r) with r min{r(x), r(x')}. This shows that U(x, r) fl U(x', r) = 0. r is a homeomorphism onto P(p(x). r). Thus (X, p) is a Riemann region over C". 44 Riemann domains r) = U(x, r), x E X, 0 < r

4). (X, p) is an F-domain of existence; (i) dense subset of 8G. It is clear that the answer is positive as long as A fl G fl aGo 0 for any G and G0 as above. This holds if, for mstance. 8G is of class Ct. To see that in the general case the situation is much more complicated, consider the following example (due to W. Jarnicki): • := (rk(1) —ra,rk(I) • k(i) is the lowest index such that rk(j) •e> 0,e, Q, is so small that c (0, 1), = 0, and < 1/4. Observe that a = to, 1j x [0,4). Take G := x (2. 3).

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Analyse Mathématique II: Calculus différentiel et intégral, séries de Fourier, fonctions holomorphes by Roger Godement


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