TITCHMARSH, EDWARD CHARLES

born June 1, 1899, Newbury, Berkshire, Eng. died Jan. 18, 1963, Oxford, Oxfordshire English mathematician whose contributions to analysis placed him in the forefront of his profession. A lecturer at University College, London, from 1923, Titchmarsh was appointed professor of pure mathematics at the University of Liverpool in 1929 and two years later became Savilian professor of geometry at the University of Oxford. He devoted his early research to the theory of Fourier integrals and series and added new findings to the study of Fourier transforms. He further contributed to the theory of conjugate functions and general integral transforms and thus formed a major part of his Introduction to the Theory of Fourier Integrals (1937). He next turned his attention to the study of the theory of integral functions, especially the Riemann zeta-function (a complex-number function), and published his results in The Zeta-Function of Riemann (1930) and more fully elaborated this work in The Theory of the Riemann Zeta-Function (1951). From his studies of complex-variable theory he wrote The Theory of Functions (1932), which became a leading textbook on real and complex function theory and was translated into numerous languages. After 1939 Titchmarsh concentrated his research on the theory of function expansion in eigenfunctions of differential equations, an area of vital importance to quantum theory, and published many of his results in Eigenfunction Expansions Associated with Second-Order Differential Equations (Part 1, 1946; Part 2, 1958). His contributions helped resolve the differences between the general theory of quantum mechanics and the methods used to solve particular problems in quantum theory.