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 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 thoughts 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 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

Get Pseudodifferential Operators and Nonlinear PDE PDF

For the prior 25 years the idea of pseudodifferential operators has performed a massive position in lots of intriguing and deep investigations into linear PDE. over the last decade, this instrument has additionally all started to yield attention-grabbing ends up in nonlinear PDE. This ebook is dedicated to a precis and reconsideration of a few used of pseudodifferential operator recommendations in nonlinear PDE.

Christopher Heil, Palle E. T. Jorgensen, David R. Larson's Wavelets, Frames and Operator Theory PDF

Some time past twenty years, wavelets and frames have emerged as major instruments in arithmetic and expertise. they have interaction with harmonic research, operator thought, and a bunch of different purposes. This e-book grew out of a distinct consultation on Wavelets, Frames and Operator idea held on the Joint arithmetic conferences in Baltimore and a countrywide technology Foundation-sponsored workshop held on the college of Maryland.

Download PDF by Niels Jacob, Kristian P Evans: A Course in Analysis - Volume I: Introductory Calculus,

Half 1 starts with an outline of houses of the genuine numbers and starts off to introduce the notions of set idea. absolutely the price and particularly inequalities are thought of in nice aspect sooner than capabilities and their easy homes are dealt with. From this the authors circulate to differential and essential calculus.

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

Sample text

It follows that αj → 0 or j 1/j → 1. 41 Let α be a positive real number. Then the sequence α1/j converges to 1. To see this, first note that the case α = 1 is trivial, and the case α > 1 implies the case α < 1 (by taking reciprocals). So we concentrate on α > 1. But then we have 1 < α1/j < j 1/j when j > α. 18 applies and the proof is complete. 42 Let λ > 1 and let α be real. Then the sequence jα λj ∞ j=1 converges to 0. To see this, fix an integer k > α and consider j > 2k. ] Writing λ = 1 + µ, µ > 0, we have that λj = (1 + µ)j > j(j − 1)(j − 2) · · · (j − k + 1) k j−k µ ·1 .

Explain. 8. Discuss convergence of the sequence j 1/j . 9. Discuss convergence of the sequence (1 + 1/j 2 )j . * * 10. Consider the sequence given by » – 1 1 1 aj = 1 + + + · · · + − log j . 2 3 j Use a picture (remember that log is the antiderivative of 1/x) to give a convincing argument that the sequence {aj } converges. The limit number is called γ. This number was first studied by Euler. It arises in many different contexts in analysis and number theory. EXERCISES 39 As a challenge problem, show that |aj − γ| ≤ C j for some universal constant C > 0.

To see this, let > 0. Choose an integer N > 0 such that |aj − ak | < /2 whenever j, k > N . 1) hence aj > aN+1 − /2 when j ≥ N + 1. Thus aN+1 − /2 ∈ S and it follows that α ≥ aN+1 − /2. 2) 24 CHAPTER 2. 1) also shows that aj < aN+1 + /2 when j ≥ N + 1 . Thus aN+1 + /2 ∈ S and α ≤ aN+1 + /2. 3) gives |α − aN+1 | ≤ /2. 4) yields, for j > N , that |α − aj | ≤ |α − aN+1 | + |aN+1 − aj | < /2 + /2 = . This proves that the sequence {aj } converges to α, as claimed. 13 Any convergent sequence is Cauchy.

Download PDF sample

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


by Paul
4.5

New PDF release: Analyse Mathématique II: Calculus différentiel et intégral,
Rated 4.14 of 5 – based on 42 votes