If en with n E N is a set of orthonormal vectors in L[a, b] then...
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If en with n E N is a set of orthonormal vectors in L[a, b] then for any function L [a, b] the following inequality holds (fn) f n=0 and equality (Parseval's formula) holds if and only if that is f = fnen, n=0 = lim ffnen = 0. N n=0 Here fn (f, en) are the Fourier coefficients of f. Hint. First, show that the following version of the Pythagoras theorem holds in infinitedimensional Hilbert spaces: If (u, v) = 0 then u2+ v = u+v. ofnen is orthogonal to f  sy and apply the Pythagoras Then use that sy = theorem.
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Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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