Alan Gaius Ramsay McIntosh (* 1942 in Sydney, † August 8, 2016 ) was an Australian mathematician who dealt with analysis (

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s). He was a professor at the

Australian National University The Australian National University (ANU) is a public research university located in Canberra, the capital of Australia. Its main campus in Acton encompasses seven teaching and research colleges, in addition to several national academies and ...

in Canberra. McIntosh studied at the University of New England with a bachelor's degree in 1962 (as a student he also received the University Medal ) and PhD in 1966 with Frantisek Wolf at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, ( Representation of Accretive Bilinear Forms in Hilbert Space by Maximal Accretive Operator ). In Berkeley, he was also a student of Tosio Kato. As a post-doctoral student, he was at the Institute for Advanced Study and from 1967 he taught at

Macquarie University Macquarie University ( ) is a public research university based in Sydney, Australia, in the suburb of Macquarie Park. Founded in 1964 by the New South Wales Government, it was the third university to be established in the metropolitan area of S ...

and from 1999 at the Australian National University. In 2014 he became emeritus. McIntosh was involved in solving the Calderon conjecture in the theory 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, who ...

s. In 2002, he solved with

Pascal Auscher Pascal Auscher is a French mathematician working at University of Paris-Sud. Specializing in harmonic analysis and operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential o ...

, Michael T. Lacey, Philipp Tchamitchian and

Steve Hofmann Steve Hofmann is a mathematician who helped solve the famous Kato's conjecture. Said Hofmann, “It's a problem that has interested me since I was a graduate student... It was one of the biggest open problems in my field and everybody thought it wa ...

the open Kato root problem for

elliptic differential operator In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that the coefficients of the highest-order derivatives be positive, which i ...

s. He also deals with

boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

s of partial differential equations with applications (such as

scattering theory In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunli ...

of the

Maxwell equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. Th ...

in irregular areas),

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result o ...

and

functional calculus In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators. It is now a branch (more accurately, several related areas) of the field of functional analysis, connected with spectral theo ...

of operators in

Banach space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...

s, analysis with

Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hyperc ...

s, barriers for the heat kernel equation and functional calculus for elliptic partial differential operators. In 1986 he became a fellow of the Australian Academy of Science, whose

Hannan Medal The Hannan Medal in the Mathematical Sciences is awarded every two years by the Australian Academy of Science to recognize achievements by Australians in the fields of pure mathematics, applied and computational mathematics, and statistical scienc ...

he received in 2015. In 2002 he received the

Moyal Medal Moyal may refer to: People *Ann Moyal (1926–2019), Australian historian *Damien Moyal (born 1976), American vocalist, musician and designer * Diana López Moyal, Cuban flutist *Eliyahu Moyal (1920–1991), Israeli politician *Esther Moyal (1874� ...

from Macquarie University.

References

Mathematical LegacyObituary notice, 2016, from the Australian Mathematical Society
1942 births 2016 deaths Australian mathematicians University of New England (Australia) alumni University of California, Berkeley alumni Academic staff of the Australian National University Academic staff of Macquarie University {{mathematician-stub