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mathematics

Jean-Pierre Kahane

Jean-Pierre Kahane is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jean-Pierre Kahane rather than just read about it. In short: Jean-Pierre Kahane (11 December 1926 – 21 June 2017) was a French mathematician with contributions to harmonic analysis. He's also credited for introducing sub-gaussian random variables.

Jean-Pierre Kahane — main illustration
Jean-Pierre Kahane — illustration

Key takeaways

  • Jean-Pierre Kahane belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Jean-Pierre Kahane to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Jean-Pierre Kahane from memory before moving on to harder problems.

Reference excerpt

Jean-Pierre Kahane (11 December 1926 – 21 June 2017) was a French mathematician with contributions to harmonic analysis. He's also credited for introducing sub-gaussian random variables.

Career Kahane attended the École normale supérieure and obtained the agrégation of mathematics in 1949. He then worked for the CNRS from 1949 to 1954, first as an intern and then as a research assistant. He defended his PhD in 1954; his advisor was Szolem Mandelbrojt. He was assistant professor, then professor of mathematics in Montpellier from 1954 to 1961. Since then, he has been professor until his retirement in 1994, then professor emeritus at the Université de Paris-Sud in Orsay. He was a Plenary Speaker at the International Congress of Mathematicians in 1962 in Stockholm and an Invited Speaker at the 1986 ICM meeting in Berkeley, California. He was elected corresponding member of the French Academy of Sciences in 1982 and full member in 1998. He was president of the Société mathématique de France, the French Mathematical Society from 1971 to 1973. In 2000 Kahane received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden In 2002 he was elevated to the rank of commander in the order of the Légion d'Honneur. In 2012 he became a fellow of the American Mathematical Society.

Activism Kahane was also known for his lifelong activism as part of the French Communist Party.

Selected publications Lectures on mean periodic functions (Bombay, Tata Institute, 1959). Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 50, Springer Verlag 1970 with Raphaël Salem: Ensembles parfaits et séries trigonométriques, Hermann, 1963, 1994 Some random series of functions, Lexington, Massachusetts, D. C. Heath 1968, 2nd edition Cambridge University Press 1985 Séries de Fourier aléatoires, Presse de l’ Université de Montreal 1967 editor with A. G. Howson: The Popularization of Mathematics, Cambridge University Press 1990 Des series de Taylor au movement brownien, avec un apercu sur le retour, in Jean-Paul Pier, Development of mathematics 1900–1950, Birkhäuser 1994

References

External links Jean-Pierre Kahane at the Mathematics Genealogy Project (in French) Bio from the French Academy of Sciences

Illustrations

Jean-Pierre Kahane illustration

Worked examples

Example 1 — a first encounter with Jean-Pierre Kahane

Start with the simplest possible case. Write down what Jean-Pierre Kahane claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jean-Pierre Kahane before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jean-Pierre Kahane ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jean-Pierre Kahane

In research
Jean-Pierre Kahane appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Jean-Pierre Kahane in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Jean-Pierre Kahane is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1926 births, 2017 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Jean-Pierre Kahane outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Jean-Pierre Kahane in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Jean-Pierre Kahane means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Jean-Pierre Kahane out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jean-Pierre Kahane in simple terms?

Jean-Pierre Kahane (11 December 1926 – 21 June 2017) was a French mathematician with contributions to harmonic analysis. He's also credited for introducing sub-gaussian random variables.

Why does Jean-Pierre Kahane matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jean-Pierre Kahane?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jean-Pierre Kahane.

Tags

  • 1926 births
  • 2017 deaths
  • 20th-century French mathematicians
  • Academic staff of Paris-Sud University
  • Fellows of the American Mathematical Society
  • French Communist Party members
  • Grand Officers of the Legion of Honour
  • Members of the French Academy of Sciences
  • Members of the Hungarian Academy of Sciences
  • Scientists from Paris
  • École normale supérieure (Paris) alumni

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