Accurate reconstructions of functions of finite regularity from truncated Fourier series expansions
Accurate reconstructions of functions of finite regularity from truncated Fourier series expansions
Knowledge of a truncated Fourier series expansion for a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 pi"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π<!-- π --></mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">2\pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-periodic function of finite regularity, which is assumed to be piecewise smooth in each period, is used to accurately reconstruct the corresponding function. An …