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Mais ne vous reveillez pas

30 December, 2018

Via Terry Tao’s blog, I just learned that Jean Bourgain passed away just before Christmas, at the relatively young age of 64.

I never met Bourgain, and have never studied in any depth many of the areas of analysis where he broke new ground and had lasting impact, but several of his papers – not even his deepest or hardest work, just ones that happened to touch on areas of interest to me – have intrigued me with varying degrees of enlightement and bafflement. Here is a non-comprehensive selection (representing only my own interests) based on a few bookmarks and some reflection off the top of my head.

A counterexample to a complementation problem
Compositio Math. (1981)

New Banach space properties of the disc algebra and H^\infty
Acta Math. (1984)

Translation invariant forms on L^p(G)(1<p<\infty )
Annales Institut Fourier (1986)

On the similarity problem for polynomially bounded operators on Hilbert space
Isr. J. Math. (1986)

A problem of Douglas and Rudin on factorization
Pacific J. Math. (1986)

On the dichotomy problem for tensor algebras
Trans. Amer. Math. Soc. (1986)

Bounded orthogonal systems and the Λ(p)-set problem
Acta Math. (1989)

Sidonicity and variants of Kaczmarz’s problem (with M. Lewko)
Annales Institut Fourier (2017)

I expect that other bloggers who are more au fait with Bourgain’s work in harmonic analysis, PDE, and additive combinatorics will say more about his impact in those areas; and those who have met him and had deeper involvement with his work will be able to offer more fitting tributes. A start is the blog post of Terry Tao which I mentioned at the start

Cette cathédrale en pierre
Traînez-la à travers bois
Jusqu’où vient fleurir la mer
Mais ne vous reveillez pas

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