Fourier Series and Integrals (Probability and Mathematical Statistics)

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text. The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier s basic series and integrals and on the astonishing variety The basic idea of Fourier series is that "any" periodic function f of, say, time can be expressed as a "trigonometric sum" of sines and cosines of the same period T:.