![\"Meyer](\"http:\/\/blogs.ams.org\/beyondreviews\/files\/2018\/03\/MeyerMathematica-300x193.png\")
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Yves Meyer<\/a> has been selected to win the 2017 Abel Prize. \u00a0The citation is “for his pivotal role in the development of the mathematical theory of wavelets”. \u00a0His work is certainly well known within mathematics, especially within harmonic analysis<\/a>\u00a0and in its important applications in image processing, data compression, signal analysis, and many other modern settings. \u00a0\u00a0<\/p>\n There are announcements of the prize in various places:<\/p>\n I will defer to these other sources\u00a0for general information about the prize and about Meyer’s work. \u00a0Here I would like to bring out a few aspects of his work with the help of Mathematical Reviews<\/em>. \u00a0First of all, at the time of this writing, there are 8448 items in MathSciNet with the word “wavelet” or “wavelets” in the title. \u00a0Looking for either “wavelet” or “wavelets” anywhere in our records for items produces\u00a013705 matches. \u00a0The earliest is<\/p>\n MR0001894<\/a>\u00a0Baker, Bevan B.; Copson, E. T.\u00a0The Mathematical Theory of Huygens’ Principle<\/em>. Oxford University Press, New York, (1939). vii+155 pp.<\/p>\n where “spherical wavelets” are mentioned in the review. \u00a0(I suspect that these are not\u00a0the same thing we normally think of as wavelets.)<\/p>\n Secondly, since citations<\/a> are a big thing these days, let me point\u00a0out that in MathSciNet, Meyer\u00a0is cited 4834 times by 3262 authors<\/a>. \u00a0His most highly cited work is, not surprisingly, about wavelets:<\/p>\n MR1228209<\/a> Meyer, Yves. Wavelets and operators<\/em>. Translated from the 1990 French original by D. H. Salinger. Cambridge Studies in Advanced Mathematics, 37. Cambridge University Press, Cambridge, 1992. xvi+224 pp. ISBN: 0-521-42000-8; 0-521-45869-2<\/p>\n This is the first part of a multi-part\u00a0book. \u00a0The second part was published as<\/p>\n MR1456993<\/a>\u00a0 Meyer, Yves; Coifman, Ronald<\/a>.\u00a0Wavelets.\u00a0 Calder\u00f3n-Zygmund and multilinear operators<\/em>. Translated from the 1990 and 1991 French originals by David Salinger. Cambridge Studies in Advanced Mathematics, 48. Cambridge University Press, Cambridge, 1997. xx+315 pp. ISBN: 0-521-42001-6; 0-521-79473-0<\/p>\n The book was published in two parts in English, but in three parts in French:<\/p>\n MR1085487<\/a> Meyer, Yves. Ondelettes et op\u00e9rateurs. I. \u00a0Ondelettes<\/em>. \u00a0Actualit\u00e9s Math\u00e9matiques. \u00a0Hermann, Paris, 1990. Meyer and Coifman have 37 joint publications<\/a> listed in MathSciNet. \u00a0 The earliest is a paper on singular integrals<\/a> published in the Transactions of the AMS<\/em>. \u00a0 Their most frequently cited joint work<\/a> is on pseudodifferential operators, and was published as a volume in the esteemed series \u00a0Ast\u00e9risque<\/em> from the\u00a0Soci\u00e9t\u00e9 Math\u00e9matique de France.<\/em><\/p>\n Meyer has published three books with the American Mathematical Society:<\/p>\n MR1342019<\/a>\u00a0Jaffard, St\u00e9phane; Meyer, Yves.\u00a0Wavelet methods for pointwise regularity and local oscillations of functions<\/em>. \u00a0Mem. Amer. Math. Soc. 123 (1996), no. 587, x+110 pp.<\/p>\n MR1483896<\/a> Meyer, Yves.\u00a0Wavelets, vibrations and scalings<\/em>. With a preface in French by the author. CRM Monograph Series, 9. American Mathematical Society, Providence, RI, 1998. x+133 pp. ISBN: 0-8218-0685-8<\/p>\n MR1852741<\/a> Meyer, Yves. Oscillating patterns in image processing and nonlinear evolution equations<\/em>. The fifteenth Dean Jacqueline B. Lewis memorial lectures. University Lecture Series, 22. American Mathematical Society, Providence, RI, 2001. x+122 pp. ISBN: 0-8218-2920-3<\/p>\n There was a story last year<\/a> about a recent result of Meyer’s. \u00a0Meyer was looking at variations on the\u00a0Poisson formula as given in the work of Nir Lev<\/a> and Alexander Olevskii<\/a>,\u00a0Quasicrystals with discrete support and spectrum.\u00a0Rev. Mat. Iberoam.<\/em> 32 (2016), no. 4, 1341\u20131352 [MR3593527<\/a>]. \u00a0After lecturing several times on the result, Meyer came up with a simpler proof of the result. \u00a0 Like any good researcher, before sending off the paper to a journal, he checked the existing literature. \u00a0In the references to the Lev and Olevskii paper, he found a paper by Guinand<\/a>:<\/p>\n MR0107784<\/a>\u00a0 Guinand, A. P.\u00a0Concordance and the harmonic analysis of sequences. \u00a0Acta Math<\/em>. 101 1959 235\u2013271.<\/p>\n Meyer dug up a copy of the paper and was surprised to find that Guinand had the same solution as his own. \u00a0But no one had noticed this. \u00a0Lev and Olevskii had not. \u00a0Nor, apparently, had Salomon Bochner<\/a>, who made no mention of it in his review of the paper in Mathematical Reviews. \u00a0Meyer adjusted his paper accordingly, giving priority to Guinand, and it was published in the Proceedings of the National Academy of Science USA:<\/p>\n MR3482845<\/a>\u00a0Meyer, Yves F. Measures with locally finite support and spectrum.\u00a0Proc. Natl. Acad. Sci. USA<\/em> 113 (2016), no. 12, 3152\u20133158.<\/p>\n In the section labeled\u00a0Significance<\/em>, Meyer wrote,\u00a0“Our new Poisson\u2019s formulas were hidden inside an old and almost forgotten paper published in 1959 by A. P. Guinand.”<\/p>\n <\/p>\n Wavelet image by JonMcLoone<\/a> – Own work<\/span>, CC BY-SA 3.0<\/a>, Link<\/a><\/p>\n\n
\nMR1085488<\/a> Meyer, Yves. Ondelettes et op\u00e9rateurs. II. Op\u00e9rateurs de Calder\u00f3n-Zygmund<\/em>. \u00a0Actualit\u00e9s Math\u00e9matiques. Hermann, Paris, 1990.
\nMR1160989<\/a> Meyer, Yves; Coifman, R. R<\/a>. Ondelettes et op\u00e9rateurs. III. Op\u00e9rateurs multilin\u00e9aires<\/em>. \u00a0Actualit\u00e9s Math\u00e9matiques. Hermann, Paris, 1991<\/p>\n
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