Harmonic Analysis

Abstract

THIS treatise contains, in an expanded form, the subject-matter of a course of lectures by Prof. Byerly, on the functions mentioned in the title. The properties of the functions are developed, to a large extent, by means of special examples of their application to obtain solutions of problems involving the differential equations of physics. The object of the treatise appears to be rather to give examples of the practical applications of the functions, than to develop in detail their analytical properties; many important theoretical points are accordingly passed over, the results of investigations being in many cases merely stated. In the introductory chapter the functions of Legendre and Bessel are introduced by means of some of the simpler differential equations of physics. As a matter of method, we think it might have been better to have referred all the functions to Laplace's equation in the first instance, leaving the cases of the equations of heat, vibrations, &c. for subsequent treatment; thus, for example, the circular and exponential functions, spherical harmonics, and Bessel's functions should make their first appearance in the normal forms,

An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics.

By W. E. Byerly, Professor of Mathematics in Harvard University. (Boston, U.S.A.: Ginn and Co.)