Celebratio Mathematica

Ant­oni Zyg­mund was one of the greatest and most in­flu­en­tial ana­lysts of this cen­tury. Among oth­er top­ics he worked on sum­mab­il­ity of nu­mer­ic­al series, sum­mab­il­ity of gen­er­al or­tho­gon­al series, tri­go­no­met­ric in­teg­rals, sets of unique­ness, sum­mab­il­ity of Four­i­er series, dif­fer­en­ti­ab­il­ity of func­tions, smooth func­tions, ap­prox­im­a­tion the­ory, ab­so­lutely con­ver­gent Four­i­er series, mul­ti­pli­ers and trans­la­tion in­vari­ant op­er­at­ors, con­jug­ate series and Taylor series, la­cun­ary tri­go­no­met­ric series, series of in­de­pend­ent ran­dom vari­ables, ran­dom tri­go­no­met­ric series, the Lit­tle­wood–Pa­ley, Lus­in and Mar­cinkiewicz func­tions, bound­ary val­ues of ana­lyt­ic and har­mon­ic func­tions, sin­gu­lar in­teg­rals, par­tial dif­fer­en­tial equa­tions and in­ter­pol­a­tion op­er­at­ors (for more de­tails see Zyg­mund’s Se­lec­ted Pa­pers, Vols. 1–3, Kluwer Aca­dem­ic Pub­lish­ers, 1989).

The list of his pub­lic­a­tions con­sists of 215 items. It in­cludes sev­er­al books, among oth­ers the clas­sic­al Tri­go­no­met­ric Series which has had sev­er­al edi­tions since 1935.

Zyg­mund was an ex­cel­lent teach­er. The list of his Ph.D. stu­dents con­tains 39 names, many of them lead­ing spe­cial­ists in vari­ous fields of math­em­at­ics.

Ant­oni Zyg­mund was born in Warsaw on 26 Decem­ber 1900 in a fam­ily of a state em­ploy­ee, he was one of four chil­dren in this fam­ily (his two sis­ters are still liv­ing in Warsaw). At the out­break of the first world war his fam­ily was evac­u­ated to Poltava (Ukraine), where he con­tin­ued his edu­ca­tion. After re­turn­ing in 1918 to (by then) in­de­pend­ent Po­land he com­pleted his sec­ond­ary edu­ca­tion and in 1919 entered Warsaw Uni­versity. Among his teach­ers was Stefan Mazurkiewicz and Wacław Si­er­piński, but it was Aleksander Ra­jch­man who had the greatest in­flu­ence upon him. Ra­jch­man dir­ec­ted his in­terest to tri­go­no­met­ric series. Zyg­mund was also in­flu­enced by his older fel­low stu­dent Stan­isław Saks. With Saks’ sup­port, in 1922 Zyg­mund was ap­poin­ted in­struct­or at the Chair of Math­em­at­ics of Warsaw Tech­nic­al Uni­versity, held by Wit­old Po­gorzel­ski. A year later Zyg­mund took his Ph.D. for his work in the Rieman­ni­an the­ory of tri­go­no­met­ric series. The de­gree was ob­tained in Warsaw Uni­versity un­der (rather form­al) guid­ance of Stefan Mazurkiewicz. In 1925 Zyg­mund mar­ried Irena Parnowska — he had met her when she was a stu­dent of math­em­at­ics at Warsaw Uni­versity. In 1926 Zyg­mund re­ceived ha­bil­it­a­tion and in 1929/30 he was awar­ded a Rock­e­feller fel­low­ship which he used for a vis­it to Eng­land. He spent half a year in Ox­ford with G. H. Hardy and half a year in Cam­bridge where he met R. E. A. C. Pa­ley; their col­lab­or­a­tion las­ted un­til Pa­ley’s ac­ci­dent­al death in 1933. Earli­er (per­haps in sum­mer 1929 on his way to Eng­land) Zyg­mund vis­ited Raphaël Salem in Par­is. Their col­lab­or­a­tion las­ted un­til Salem’s death in 1957. In 1930 Zyg­mund was offered a chair of math­em­at­ics at the Stefan Bat­ory Uni­versity in Wilno. In Wilno he met Józef Mar­cinkiewicz, by then a first year stu­dent of math­em­at­ics, and one of the most prom­ising math­em­aticians Po­land ever had. Their col­lab­or­a­tion las­ted un­til the out­break of the second world war.

In 1935 Zyg­mund pub­lished his first book Tri­go­no­met­ric­al Series. The book has had sev­er­al edi­tions and is one of the most im­port­ant and in­flu­en­tial books in this field. In 1938 he pub­lished a book on ana­lyt­ic func­tions (in Pol­ish) writ­ten jointly with Stan­isław Saks. For this book the au­thors re­ceived in 1939 an award of the Pol­ish Academy of Learn­ing in Cra­cow. Both books were pub­lished in the series “Mono­grafie Matematyczne” cofoun­ded by Stefan Banach. At the out­break of the war Zyg­mund was mo­bil­ized as a re­serve of­ficer. After the Pol­ish Army’s de­feat Zyg­mund suc­ceeded in re­turn­ing to Wilno and leav­ing Po­land through Sweden for the United States to­geth­er with his wife and son. He worked there in MIT, Mount Holy­oke Col­lege, Uni­versity of Pennsylvania in Phil­adelphia, and since 1947 un­til his re­tire­ment in 1980 at the Uni­versity of Chica­go (since 1964 as a Dis­tin­guished Ser­vice Pro­fess­or of Math­em­at­ics). Zyg­mund’s wife Irena died in 1966 and his son was killed in a plane ac­ci­dent in 1983. He is sur­vived by four grand­sons liv­ing in Eng­land.

Zyg­mund trav­elled a lot. He at­ten­ded all post­war con­gresses of math­em­aticians (with an in­vited ad­dress dur­ing the 1954 Con­gress in Am­s­ter­dam), twice held a vis­it­ing po­s­i­tion in Ar­gen­tina and fre­quently vis­ited Eng­land, France and Po­land.

Pro­fess­or Ant­oni Zyg­mund was awar­ded many hon­ours. He had hon­or­ary de­grees from Wash­ing­ton Uni­versity, Uni­versity of Tor­uń, Uni­versity of Par­is and Uni­versity of Uppsala. He was a mem­ber of the Pol­ish Academy of Sci­ences (1959), Na­tion­al Academy of Sci­ences of the United States (1961), Ar­gen­tini­an Academy of Sci­ences (1964), Roy­al Academy of Sci­ences in Mad­rid and Academy of Arts and Sci­ences in Palermo (1967). Zyg­mund was a hon­or­ary mem­ber of the Lon­don Math­em­at­ic­al So­ci­ety (1967) and of the Pol­ish Math­em­at­ic­al So­ci­ety (1972). He re­ceived the Gug­gen­heim Found­a­tion fel­low­ship (1953/54), the Award of the Al­fred Jurzykowski Found­a­tion (1972) and the Steel Prize of the Amer­ic­an Math­em­at­ic­al So­ci­ety (1979). In 1986 he was dec­or­ated with the Na­tion­al Medal of Sci­ence (USA).

Since 1968 Zyg­mund had served as a mem­ber of the Ed­it­or­i­al Com­mit­tee of this journ­al. He was one of the most act­ive mem­bers of the Com­mit­tee help­ing us of­ten with his ad­vice. The present shape of the journ­al owes him a lot.

Ant­oni Zyg­mund died in Chica­go on 30 May 1992 and was bur­ied there on 2nd June.