Heinz Otto Cordes (March 18, 1925 – October 30, 2018) was a German-American mathematician, specializing in

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s (PDEs). He is known for the Aronszajn–Cordes uniqueness theorem for solutions of elliptic PDEs (due independently to

Nachman Aronszajn Nachman Aronszajn (26 July 1907 – 5 February 1980) was a Polish American mathematician. Aronszajn's main field of study was mathematical analysis, where he systematically developed the concept of reproducing kernel Hilbert space. He also contrib ...

Biography

At the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

, Cordes received in 1952 his doctorate. His doctoral dissertation, supervised by

Franz Rellich Franz Rellich (September 14, 1906 – September 25, 1955) was an Austrian-German mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differen ...

, is entitled ''Separation von Variablen in Hilbertschen Raumen'' (Separation of variables in

Hilbert space In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...

s). Cordes held a junior academic appointment at Göttingen from 1952 to 1956, when he was appointed to an assistant professorship at the

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...

. At the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

(UC Berkeley), he was an assistant professor to 1958 to 1959, an associate professor from 1959 to 1963, and a full professor from 1963 to 1991, when he retired as professor emeritus. In retirement he remained active in research. Cordes made a number of significant contributions to the theory of PDEs. He also introduced

C*-algebra In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of contin ...

techniques to define the symbol of elements of algebras of

singular integral operator In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator : T(f)(x) = \int K(x,y)f(y) \, dy, wh ...

s (as well as algebras of

pseudodifferential operators In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in m ...

). Thereby he extended the operator symbol calculus from compact manifolds to various classes of non-compact manifolds. This research led him to study

Dirac operator In mathematics and in quantum mechanics, a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as a Laplacian. It was introduced in 1847 by William Ham ...

s with their connections with relativistic quantum mechanics. He was the author of 4 books and the author or co-author of more than 60 articles. From 1963 to 1999, he sometimes collaborated with

Tosio Kato was a Japanese mathematician who worked with partial differential equations, mathematical physics and functional analysis. Education and career Kato studied physics and received his undergraduate degree in 1941 at the Imperial University of To ...

. Cordes received an Alfred P. Sloan fellowship in 1959. He declined an invitation to address the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

held in Moscow in 1966. For the academic year 1971–1972, Cordes was a visiting professor at

Lund University Lund University () is a Public university, public research university in Sweden and one of Northern Europe's oldest universities. The university is located in the city of Lund in the Swedish province of Scania. The university was officially foun ...

, where he gave a course on pseudodifferential operators via a C*-algebra approach. His 19 doctoral students at UC Berkeley include

Michael G. Crandall Michael Grain Crandall (born November 29, 1940, in Baton Rouge, Louisiana) is an American mathematician, specializing in differential equations. Mathematical career In 1962 Crandall earned a baccalaureate in engineering physics from Universit ...

and Michael E. Taylor. Upon his death in 2018, Heinz Cordes had been married to his wife Hillgia for 63 years. They were the parents of a son and two daughters.

Selected publications

Articles

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Books

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as editor

References

{{DEFAULTSORT:Cordes, Heinz Otto 1925 births 2018 deaths 20th-century German mathematicians 21st-century German mathematicians 20th-century American mathematicians 21st-century American mathematicians University of Göttingen alumni University of California, Berkeley faculty Partial differential equation theorists Operator theorists German mathematical physicists People from North Rhine-Westphalia German emigrants to the United States