#### Alberto Calderon, 77, Pioneer Of Mathematical Analysis

Alberto Calderon, one of the leading mathematicians of the last half-century, died on Thursday in Northwestern Memorial Hospital in Chicago. He was 77 and was professor emeritus of mathematics at the University of Chicago and lived in Chicago.

Mr. Calderon was known for his contributions to mathematical analysis, the branch of mathematics that includes calculus, infinite series and the analysis of functions -- helping to explain the physical universe by attaching numbers to its functions.

''He was one of the most original and profound mathematical analysts of the past 50 years,'' said Felix Browder, a professor emeritus of mathematics at the University of Chicago.

Elias M. Stein, a mathematics professor at Princeton University, said that Mr. Calderon made ''remarkable, lasting contributions in developing singular integrals that are crucial to pure mathematics and understanding physical functions, from how heat is conducted to how sound is transmitted and electromagnetic waves travel.''

He did much of his work on his own in the 1960's and later, but collaborated earlier with his mentor, Antoni Zygmund, with whom he founded what mathematicians call the Chicago school of analysis.

Robert Fefferman, chairman of the mathematics department at the University of Chicago, said their work was ''one of the most important developments in analysis in the 20th century.''

President George Bush presented Mr. Calderon with the National Medal of Science in 1991. Mr. Calderon received the Wolf Prize, the highest award in mathematics, in 1989.

Singular integrals helped provide science and industry with a way to make widespread use of Fourier analysis, named after its creator, Baron Jean Baptiste Joseph Fourier, an early 19th-century French mathematician. The baron discovered that physical functions could be described mathematically, like describing the conduction of heat as the number of oscillations per unit of length or sound as the number of wave cycles per second.

''Calderon was one of the central links'' between two major branches of mathematics, Mr. Browder said, ''Fourier analysis and partial differential equations.''

These equations govern, or predict, functions of physical phenomena, like heat, sound and electromagnetism. And the Calderon-Zygmund theory of singular integrals helped find the unknown from the known, helped infer the unknown from available information.

Alberto Calderon was born in Argentina on Sept 14, 1920. His early education was in Switzerland, and he received a civil-engineering degree at the University of Buenos Aires in 1947. It was in a seminar there that Mr. Calderon's brilliance was discovered. Antoni Zygmund was discussing a proof of a classical theory he had included in a book. The student asked why the proof discussed in the seminar was so much longer than the one in the book. No, the professor said, they were identical.

It turned out that Alberto Calderon had the habit of trying difficult proofs on his own and then checking them with the professor's writings. He had forgotten to check with the Zygmund text, and assumed his own more elegant version had also been the professor's. It was not, and Professor Zygmund brought Mr. Calderon with him to Chicago in 1949, and Mr. Calderon completed his doctorate with remarkable speed, in 1950.

Mr. Calderon became visiting professor at Ohio State University, visiting member of the Institute for Advanced Study in Princeton and returned, in 1959, to Chicago. He was an honorary professor at the University of Buenos Aires; a member of the National Academy of Sciences; the American Academy of Arts and Sciences; the National Academy of Exact, Physical and Natural Sciences in Argentina; the Academie des Sciences in France; the Royal Academy of Sciences in Spain; the Latin American Academy of Sciences in Venezuela, and the Third World Academy of Science in Italy.

He is survived by his wife, Alexandra Bellow, a retired mathematician at Northwestern University, whom he married in 1989; and two children from his first marriage, Mary Josephine, of St. Charles Ill., and Pablo, of New York. His first wife, Mabel Wells Calderon, died in 1985.

By HOLCOMB B. NOBLE, April 20, 1998 © The New York Times Company