Person: Zygmund, Antoni Szczepan
Zygmund's work in harmonic analysis has application in the theory of waves and vibrations. He also did major work in Fourier analysis and its application to partial differential equations.
Mathematical Profile (Excerpt):
- Antoni continued his education in Poltava then, in 1918, he returned to Poland which had become an independent country for the first time in well over 100 years.
- At the University of Warsaw Zygmund was taught by, and very much influenced by, Janiszewski, Mazurkiewicz and Sierpiński.
- Zygmund, however, was most influenced by Aleksander Rajchman and by Stanisław Saks who had been his school friend, although three years older than he was.
- This gave Zygmund a life-long interest in the trigonometric series.
- There was a forced break in Zygmund's studies in 1920 when he was called up for the army.
- Zygmund obtained his Ph.D. from the University of Warsaw in 1923 for a dissertation on the Riemannian theory of trigonometric series written under Aleksander Rajchman's supervision.
- In 1926 Zygmund submitted his habilitation dissertation to the University of Warsaw and began teaching there.
- In going to Vilnius, Zygmund was going into a disputed city.
- This was the situation when Zygmund was appointed to the chair of mathematics there.
- In 1939 Zygmund was drafted into the Polish army as a reserve officer at the start of the Second World War.
- Zygmund returned to Vilnius but then, on 10 October 1939, Vilnius was returned to Lithuania.
- Zygmund brought Calderón back to Chicago, where he obtained his doctorate under Zygmund's supervision not too long after his arrival.
- Not only did Zygmund have the role of Calderón's teacher and advisor, but was also his mentor and became his main collaborator.
- Zygmund worked in analysis, in particular in harmonic analysis.
- Zygmund's early work, as one might expect, continued to develop ideas from his doctoral studies with Aleksander Rajchman.
- After meeting Paley at Cambridge in 1930-31, Zygmund wrote five joint papers with him, and both of them together with Norbert Wiener wrote Notes on random functions (1933).
- The joint Zygmund-Paley work played an important role in Zygmund's book Trigonometric Series (1935).
- In 1950, not long after beginning his long association with the University of Chicago, Zygmund published Trigonometric Interpolation.
- We mentioned earlier in this article Zygmund's collaboration with Calderón.
- Their joint work began with Calderón's doctoral thesis which answered some questions related to boundary behaviour of harmonic functions which had been posed by Zygmund earlier.
- Together with Richard L Wheeden, Zygmund wrote Measure and integral (1977).
- Zygmund received many honours for his outstanding achievements.
- Zygmund suffered many sad losses during his life.
- Rajchman, Zygmund's doctoral supervisor, was executed by the Nazis.
Born 25 December 1900, Warsaw, Russian Empire (now Poland). Died 30 May 1992, Chicago, Illinois, USA.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive