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Remembering Paul Turán

✍ Scribed by Richard Askey


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
129 KB
Volume
86
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis


yet his mathematics is still as fresh as when he did it. Primarily this is because Tura n frequently looked at problems from a new point of view. I have heard this expressed by those who knew his work in areas I know well as well as in areas I do not understand at all. This often means that it will take decades to decide on the real worth of some of his contributions, so we should not rush to judge that which we still do not completely understand.

In Tura n's ``Collected Papers,'' there are two interesting articles on him and his mathematics by Paul Erdo s and Ga bor Hala sz. However, neither one comments on an important aspect of Tura n's service to mathematics, namely, his editing of the selected papers of Alfre d Re nyi and the collected papers of Leopold Feje r. Here is a little on why this was important.

Feje r was the founder of the Hungarian school of analysis. A remarkable group of analysts came through this school. George Po lya wrote of Gabor Szego , We were both influenced, like all other young Hungarian mathematicians of that time, by Leopold Feje r.'' This was about 1910 to 1915. Twenty years later Tura n was also heavily influenced by Feje r. He remarks on this in the lecture he gave at the 70th anniversary meeting of the births of Feje r and Frederick Riesz. To show the style that Tura n used, after commenting that Feje r's refined techniques would often do in a few lines what others did in pages, he remarked that to use the same word calculation'' for both was analogous to the use in Hungarian of the same word for the clumsy hopping of a bear and a ballerina's pirouettes.

I have used the Feje r papers often. Tura n's editing was remarkable. He commented on many of the papers, setting them into context and telling what has happened to the ideas Feje r introduced. For example, the comments on Feje r's great work on (C, 1) summability on Fourier series include references from H. Lebesgue's 1906 book to a paper on abstract ergodic theorems by W. F. Ebelein in 1949. One interesting remark which I had not known is that Feje r's name was misspelled ``Teje r'' in both the journal and in the review in Fortschritte der Mathematik.

Another instance of the care that Tura n took is given in his Das Leben von Leopold Feje r'' which starts the first volume. He quotes Hardy about this result of Feje r as follows: .. . this fundamental result has been the starting point of a mass of modern research.'' Tura n's citation of this is from article no. 0066 253


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