The Art of TaxidermyeBook - 2013
General functions can be expanded in a series of functions that are solutions of second order differential equations. These solutions are considered to be 'eigenfunctions' (characteristic functions), which, individually, may have a particular physical property (the eigenvalue). The most common use of this technique is Fourier series, in which functions are decomposed into waves of various frequencies. Also common is the application in quantum mechanics, in which particular eigenfunctions may have defined energies or momentums. Titchmarsh considers the more general applications to be well-known, and focuses this work particularly on the 'singular' case, and intends his audience to be mathematicians rather than physicists. Contents include: The Sturm-Liouville Expansion; The Singular Case: Series Expansions; The General Singular Case; Examples; The Nature of the Spectrum; A Special Convergence Theorem; The Distribution of the Eigenvalues; Further Approximation to N(?); Convergence of the Series Expansion Under Fourier Conditions; Summability of the Series Expansion.
Publisher: [United States] : Read Country Book : Made available through hoopla, 2013
Characteristics: 1 online resource