in the expansion of a function defined on a space with respect to an orthogonal system of real-valued (complex-valued) functions on . If is an orthogonal system in a Hilbert (pre-Hilbert) space, then, given an element of this space, the numbers are also called the Fourier coefficients of with respect to the system . J. Fourier first investigated trigonometric series with coefficients defined by (*).
|||S. Kaczmarz, H. Steinhaus, "Theorie der Orthogonalreihen" , Chelsea, reprint (1951)|
Fourier coefficients. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fourier_coefficients&oldid=17816