Regarded as a result of the activity of many mathematicians of the 20th century in the field of classical Fourier series and the theory of approximation of periodic functions, the key point of this monograph is the classification of periodic functions and developed methods that enable one to solve traditional problems of approximation theory.

Résumé
This is the first comprehensive study of what remains of the writings of Aristotle's student Eudemus of Rhodes on the history of the exact sciences. These fragments are crucial to our understanding of the content, form, and goal of the Peripatetic historiography of science. The first part of the book presents an analysis of those trends in Presocratic, Sophistic and Platonic thought that contributed to the development of the history of science. The second part provides a detailed study of Eudemus' writings in their relationship with the scientific literature of his time, Aristotelian philosophy and the other historiographic genres practiced at the Lyceum: biography, medical and natural-philosophical doxography. Although Peripatetic historiography of science failed in establishing itself as a continuous genre, it greatly contributed both to the birth of the Arabic medieval historiography of science and to the development of this genre in Europe in the 16th-18th centuries.

Contenu

i-iv -- Contents -- PREFACE -- PART I -- 1. REGULARITY OF LINEAR METHODS OF SUMMATION OF FOURIER SERIES -- 2. SATURATION OF LINEAR METHODS -- 3. CLASSES OF PERIODIC FUNCTIONS -- 4. INTEGRAL REPRESENTATIONS OF DEVIATIONS OF POLYNOMIALS GENERATED BY LINEAR PROCESSES OF SUMMATION OF FOURIER SERIES -- 5. APPROXIMATION BY FOURIER SUMS IN SPACES C AND L1 -- BIBLIOGRAPHICAL NOTES (PART I) -- REFERENCES (PART I) -- PART II -- 6. CONVERGENCE RATE OF FOURIER SERIES AND THE BEST APPROXIMATIONS IN THE SPACES Lp -- 7. BEST APPROXIMATIONS IN THE SPACES C AND L -- 8. INTERPOLATION -- 9. APPROXIMATIONS IN THE SPACES OF LOCALLY SUMMABLE FUNCTIONS -- 10. APPROXIMATION OF CAUCHY-TYPE INTEGRALS -- 11. APPROXIMATIONS IN THE SPACES Sp -- 12. APPROXIMATIONS BY ZYGMUND AND DE LA VALLÉE POUSSIN SUMS -- BIBLIOGRAPHICAL NOTES (PART II) -- REFERENCES (PART II) -- Index