Bessel’s inequality

Let ( , be an inner product defined on a space X, and

[Pg.311]

If we recall the Fourier analysis, we understand that f = (/, are the Fourier coefficients. Note that Bessel s inequality (C.18) is reduced to an equality if we have... 

As it follows from these inequalities, the argument of Bessel s function in the expression (21) is very small, and coth(fku/2kT) 1. The resulting formula can be deduced, if we take into account that AE/hat — p, where p is integer and Ip(x) = I-P(x) [14],... 

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