Leçons d’analyse classique: exposition d'un cours fait par Paul Koosis à l'Université McGill, Montréal
Bibliographic record
Abstract
Ce livre est basé sur un cours de deuxième cycle donné en 2005-2006 par M. Paul Koosis, professeur émérite à l'université McGill. Il traite de sujets soigneusement choisis par le professeur à l'intention de ceux qui, plutôt que de rechercher un catalogue exhaustif de résultats techniques et abstraits, veulent être initiés aux découvertes les plus essentielles et prolifiques de l'analyse classique du vingtième siècle. Analyse harmonique, quasi-analyticité, zéros des fonctions entières (dont une preuve inédite du théorème de Levinson-Cartwright), approximation pondérée, principe d'incertitude, mesures harmoniques…, les résultats saillants et géniaux de l'analyse classique sont présentés dans un style soigné, rigoureux et détaillé, préparant les étudiants à des études plus poussées ; et au service du lecteur qui, connaissant les bases de la théorie de la mesure et de l'analyse complexe, désire suivre le merveilleux développement de M. Koosis et accroître sa connaissance du sujet. Je reconnais les choix et le style de Paul Koosis, et j'aime beaucoup les deux. Le titre est volontairement modeste et hors-mode; ce qui fait l'originalité du livre est que, sous l'apparence du "classique", il échappe complètement aux modes actuelles. Il ne me parait pas avoir d'équivalent, en aucune langue. C'est un beau cadeau au français… -Jean-Pierre Kahane, Université Paris-Sud Orsay, France This book is based on a graduate course given in 2005-2006 by Paul Koosis, Emeritus Professor at McGill University. It addresses topics carefully selected by Prof. Koosis and is intended for those who, far from seeking an exhaustive catalog of technical and abstract results, prefer to be initiated in the most essential and prolific discoveries of the 20th century in classical analysis. Harmonic analysis, quasi-analyticity, zeroes of classes of entire functions (including a new proof of the Levinson-Cartwright theorem), weighted approximation, gap theorems, harmonic measures, and other gems of classical analysis are presented in a rigorous, detailed, and elegant style. This work prepares students for more advanced studies and serves readers who, aware of the basics in measure theory and complex analysis, wish to follow Prof. Koosis in his marvelous development of the subject. I recognize the choice and style of Paul Koosis, and I greatly appreciate both. The title is intentionally modest and out of fashion; the originality of the book is that, under the guise of the "classic", it completely avoids the current fashions. It does not appear to me to have its equivalent in any language. It is a beautiful gift to the French language… -Jean-Pierre Kahane, Université Paris-Sud Orsay, France.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.008 |
| Science and technology studies | 0.006 | 0.010 |
| Scholarly communication | 0.009 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.020 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".