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In this thesis he studied the representation of arbitrary functions by the eigenfunctions of partial differential equations and other given sets of functions.
In these papers a special role is played by expansions in terms of the eigenfunctions of linear differential operators.
Within the next three years Stone published 10 more papers on various aspects of the theory of orthogonal expansions, especially expansions in terms of eigenfunctions of linear differential equations.
In those cases, we see two eigenfunctions with approximately the same statistical wavelength and usually with similar eigenvalues and relative spectral power.
From 1939 Titchmarsh concentrated on the theory of series expansions of eigenfunctions of differential equations, work which helped to resolve problems in quantum mechanics.
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