Celebratio Mathematica

Alberto Pedro Calderón

Analysis  ·  U Chicago

A tribute to Alberto Pedro Calderón

In this Chapter:

Al­berto Pedro Calderón, who died April 16, 1998, was one of this cen­tury’s lead­ing math­em­aticians. His work (mainly in the field of math­em­at­ic­al ana­lys­is) was char­ac­ter­ized by its tre­mend­ous ori­gin­al­ity and depth and its re­mark­able power. His con­tri­bu­tions have been of ex­tremely wide scope and have changed the way re­search­ers ap­proach, and think of, a wide vari­ety of areas in both pure math­em­at­ics and its ap­plic­a­tions to sci­ence. His fun­da­ment­al in­flu­ence is felt strongly in ab­stract fields, such as har­mon­ic ana­lys­is, par­tial dif­fer­en­tial equa­tions, com­plex ana­lys­is, and geo­metry, as well as in more con­crete areas, such as sig­nal pro­cessing, geo­phys­ics, and tomo­graphy. Calderón was born in Men­d­oza, Ar­gen­tina, on Septem­ber 14, 1920. He re­ceived his early edu­ca­tion there and in Switzer­land. His ini­tial pro­fes­sion­al train­ing was as a civil en­gin­eer at the Uni­versity of Buenos Aires (gradu­ated 1947), and he worked as an en­gin­eer for a few years. He sim­ul­tan­eously nur­tured his pas­sion for math­em­at­ics, partly un­der the guid­ance of Dr. Al­berto González Domínguez. Two events changed his fu­ture: His su­per­visor at YPF (the state-owned pet­ro­leum com­pany) made his life very dif­fi­cult, and around the same time, Ant­oni Zyg­mund, one of the world’s lead­ing math­em­at­ic­al ana­lysts of the time and a pro­fess­or at the Uni­versity of Chica­go, vis­ited Ar­gen­tina in 1948 at the in­vit­a­tion of Dr. González Domínguez. Zyg­mund im­me­di­ately re­cog­nized Calderón’s bril­liance, and he in­vited Calderón to come to Chica­go to work with him. Calderón ar­rived in Chica­go in 1949, as a Rock­e­feller Fel­low, and by 1950 he had ob­tained his Ph.D. in math­em­at­ics un­der Zyg­mund’s su­per­vi­sion. Calderón’s dis­ser­ta­tion was mar­velous. In it he solved three sep­ar­ate and long­stand­ing prob­lems. From this point on, Calderón and Zyg­mund star­ted one of the most suc­cess­ful col­lab­or­a­tions in math­em­at­ic­al his­tory. To­geth­er they cre­ated the mod­ern the­ory of sin­gu­lar in­teg­rals, which has had enorm­ous con­sequences for many areas of math­em­at­ics. They de­veloped what has be­come known as the “Chica­go school of ana­lys­is”, one of the most in­flu­en­tial forces in pure math­em­at­ics, which has also had a great im­pact on ap­plic­a­tions to sci­ence and en­gin­eer­ing. Calderón went on to ap­ply sys­tem­at­ic­ally the the­ory of sin­gu­lar in­teg­rals (and the im­port­ant re­fine­ments that he ob­tained) to the study of par­tial dif­fer­en­tial equa­tions. Calderón’s con­tri­bu­tions to their study have com­pletely changed the land­scape of that field. He not only solved fun­da­ment­al spe­cif­ic prob­lems but, in ad­di­tion, de­veloped a host of tech­niques that are now ba­sic to the sub­ject. Among his in­flu­en­tial achieve­ments were works on the bound­ary be­ha­vi­or of har­mon­ic func­tions, er­god­ic the­ory, the Calderón–Zyg­mund de­com­pos­i­tion, the real-vari­able the­ory of sin­gu­lar in­teg­ral op­er­at­ors, com­plex in­ter­pol­a­tion, unique­ness in the Cauchy prob­lem, bound­ary value prob­lems for el­lipt­ic equa­tions, com­mut­at­ors of op­er­at­ors hav­ing min­im­ally reg­u­lar coef­fi­cients, \( \mathrm{L}^2 \) bounded­ness of pseudodif­fer­en­tial op­er­at­ors, real vari­able Hardy space the­ory, the Cauchy in­teg­ral, and an in­verse bound­ary prob­lem in elec­tric­al pro­spec­tion.

Be­sides his re­mark­able re­search ac­com­plish­ments, Calderón was also a gif­ted teach­er. Dur­ing his ca­reer he taught at Ohio State Uni­versity, MIT, the Uni­versity of Buenos Aires, and the Uni­versity of Chica­go. He had many Ph.D. stu­dents, both in the U.S. and in Ar­gen­tina. In Ar­gen­tina he also served for sev­er­al years as dir­ect­or of the In­sti­tuto Ar­gen­tino de Matemática (IAM). Calderón was re­cog­nized all over the world for his out­stand­ing con­tri­bu­tions to math­em­at­ics. He was a mem­ber of the Na­tion­al Academy of Sci­ences of the U.S., Ar­gen­tina, Spain, and France; of the Lat­in Amer­ic­an Academy of Sci­ences; of the Academy of Sci­ences of the Third World; and of the Amer­ic­an Academy of Arts and Sci­ences. He re­ceived hon­or­ary doc­tor­ates from the Uni­versity of Buenos Aires, the Tech­nion (Is­rael), the Ohio State Uni­versity, and the Uni­ver­sid­ad Autónoma de Mad­rid. He gave many in­vited ad­dresses to uni­versit­ies and to learned so­ci­et­ies, and he was awar­ded many prizes. Among these are the Bôcher Prize (1979) and the Steele Prize (1989) from the Amer­ic­an Math­em­at­ic­al So­ci­ety, and the Wolf Prize in Math­em­at­ics (1989) from Is­rael. In 1992 Pres­id­ent Bush awar­ded him the Na­tion­al Medal of Sci­ence, the U.S.’s highest award for sci­entif­ic achieve­ment.

— Car­los E. Kenig