Analyse Mathématique II: Calculus différentiel et intégral, by Roger Godement

By Roger Godement

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 l. a. 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 options de calcul, aspect 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 type inimitable de l'auteur, et pas seulement par son refus de l'écriture condensée en utilization dans ce nombreux manuels.

Show description

Read or Download Analyse Mathématique II: Calculus différentiel et intégral, séries de Fourier, fonctions holomorphes PDF

Best functional analysis books

The Blocking Technique, Weighted Mean Operators and Hardy’s Inequality

This e-book offers the 1st accomplished therapy of the blockading method which is composed in remodeling norms in part shape into norms in block shape, and vice versa. Such norms look all through research. The blockading method is a strong, but hassle-free, instrument whose usefulnes is established within the e-book.

The Elements of Operator Theory

"The writer endeavors to provide the ideas and concepts as a substitute to the computational process, attempting to keep away from lengthy calculations by means of stressing the mathematical recommendations in the back of the statements. . . . many difficulties [are] acknowledged in the course of the booklet, quite often followed by means of tricks. "—Mathematical reports (review of the 1st edition)"This is a rigorous, logically well-organized textbook proposing uncomplicated rules and undemanding concept of operators.

Theory of Functions of a Complex variable, Volume One

This booklet is a translation by way of F. Steinhardt of the final of Caratheodory's celebrated textual content books, Funktiontheorie, quantity 1.

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

Sample text

36) which holds for all functions u ∈ C01 (Rn ) (compactly supported C1 -functions). 34) for these functions. 24. 34) are important in the theory of Newtonian spaces or more general function spaces on metric spaces. e. x, y ∈ Rn . Here M(ρ ) is the Hardy–Littlewood maximal function of ρ . e. e. and Cg can (essentially) be used as a p-weak upper gradient of u. ˜ See [101,103, 107, 291] for more details. 9. For 0 < r ≤ R and x ∈ Rn , IB(x,r) ( f )(x) ≤ Cr1/n MR ( f )(x). Proof. Set Now A j = B(x, 2− j r) \ B(x, 2− j−1 r), j = 0, 1, .

20. 32), one has to assume that f is ACLn . For a more detailed discussion; see [193]. 12. 31), fix a family Γ of paths in D. Since f is ACLn , the Fuglede theorem implies that f (the coordinate functions of f ) is absolutely continuous on a path family Γ0 of n-almost all paths in Γ . Then Mn (Γ0 ) = Mn (Γ ). We need to show that Mn (Γ0 ) ≤ KMn ( f Γ ). To this end, let ρ be an admissible function for f Γ . Write ρ ( f (x))L(x, f ), x ∈ D, ρ (x) = x ∈ D, 0, where L(x, f ) = lim sup y→x | f (y) − f (x)| .

5 that Mn ( f −1Γ ) ≥ Mn (Γ ) ≥ C = C(n) > 0, where Γ is the family of all paths joining E to F in B(x, 4r0 ). By the quasiconformality of f , C ≤ Mn ( f −1Γ ) ≤ KMn (Γ ) ≤ ωn−1 (log(L/l))1−n , and hence L(x, f , r)/l(x, f , r) = L/l ≤ C = C(n, K) . Letting r → 0, we see that H(x, f ) ≤ C(n, K), as required. 26. For n = 2, C(2, K) is known; see [190]. The value C(n, K), n ≥ 3, was found very recently; see [285]. 3)]. 3) satisfies H(x, f ) ≤ C(n, K) < ∞ at each point x ∈ D. Now it turns out that a more global version than H(x, f ) ≤ C < ∞ is true for quasiconformal maps f .

Download PDF sample

Rated 4.67 of 5 – based on 5 votes