Shmuel Agmon

Shmuel Agmon (; 2 February 1922 – 21 March 2025) was an Israeli mathematician who was known for his work in analysis and partial differential equations.

Biography Shmuel Agmon was born in Tel Aviv, in what was then British-ruled Mandatory Palestine, to Nathan and Chaya Agmon (née Gutman). His father was a prominent writer and his mother was a dentist. Agmon spent the first two years of his life living in Nazareth, where his mother ran a clinic, before the family moved to Jerusalem, where his younger brother Yaakov was born in 1924. He was identified as a gifted child in school, excelling in mathematics and classical literature. He was also a Jerusalem youth chess champion. A member of the HaMahanot HaOlim youth movement, Agmon attended high school at the Rehavia Gymnasium and after graduating he joined a hakhshara program at kibbutz Na'an in 1939.

He began his studies in mathematics at the Hebrew University of Jerusalem in 1940. His teachers included Michael Fekete, Abraham Fraenkel, Binyamin Amirà, and Jakob Levitzki. In 1942, Agmon interrupted his studies and enlisted in the British Army, serving in an anti-aircraft unit and then the Jewish Brigade. He served for four years in Palestine, Cyprus, Italy, and Belgium during and immediately after World War II. While on leave in Paris after the war, he purchased works by French mathematician Édouard Goursat from a local bookstore to resume studying mathematics. He then went to the United States and worked as a visiting scholar at Rice University from 1950 to 1952 before returning to Jerusalem. He joined the faculty of the Hebrew University of Jerusalem in 1952 and became a full professor in 1959. He was elected to membership in the Israel Academy of Sciences and Humanities in 1964.

Agmon died on 21 March 2025, at the age of 103.

Work After joining the Hebrew University in 1952, Agmon initially taught a course on partial differential equations. He worked on aspects of elliptic-hyperbolic equations in the 1950s, including the Euler–Tricomi equation. He collaborated with Louis Nirenberg and Avron Douglis in producing two groundbreaking works on elliptic partial differential boundary value problems in 1959 and 1964 that became among the most cited works in mathematical analysis. Agmon's contributions to partial differential equations include Agmon's method for proving exponential decay of eigenfunctions for elliptic operators. In 1965 he published a book on linear boundary value problems for elliptic partial differential equations of general order that became a foundational work in the field. He also taught an advanced undergraduate course on classical analysis. From the mid-1960s, he worked on spectral theory and scattering theory of Schrödinger-type equations, publishing works significant to mathematical physics. Notably, he made precise estimates on the decay of Eigenfunctions of the Schrödinger equation in terms of a metric he defined, which became known as the Agmon metric. His work contributed to the understanding of wave function scattering for short range and long range potentials.

Awards Agmon was awarded the 1991 Israel Prize in mathematics. He received the 2007 EMET Prize "for paving new paths in the study of partial-elliptical differential equations and their problematic language and for advancing the knowledge in the field, as well as his essential contribution to the development of the Spectral Theory and the Distribution Theory of Schrödinger Operators." He has also received the Weizmann Prize and the Rothschild Prize.

Selected works

with Lipman Bers: