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Results tagged with ca.classical-analysis-and-odes
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user 14971
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Convergence of squares of the moduli of partial sums of Fourier series
Let $\mu$ be a complex measure on the unit circle. The Wiener theorem says that the sequence of the Cesaro means of $|\hat\mu_n|$ has a limit. Define $p_n(z)=\sum_{k=0}^n \hat\mu_k z^k$. Then the Abel …
CommunityBot
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Convergence of squares of the moduli of partial sums of Fourier series
Let my answer be as above, namely, if $\mu$ has no point masses, then we get squared moduli of the limits of the boundary values of the Cauchy tramsforms of $\mu$. For the purely point part of $\mu$ o …
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