Diophantine approximation and convergence of alternating series
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- by N. V. Rao PDF
- Proc. Amer. Math. Soc. 93 (1985), 420-422 Request permission
Abstract:
Let $f$ be a continuous periodic function of period $2\pi$ and \[ \sum {(|{a_n}| + |{b_n}|)\log n < \infty } ,\] where ${a_n},{b_n}$ are the Fourier coefficients of $f$. Let $E$ be the set of all points $\theta$ in $[0,2\pi )$ for which the series \[ \sum {\frac {{{{( - 1)}^n}}}{n}f(n\theta )} \] does not converge. It is established here that hausdorff outer measure ${h_\alpha }(E) = 0$ for every $\alpha > 0$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 420-422
- MSC: Primary 11K60
- DOI: https://doi.org/10.1090/S0002-9939-1985-0773994-4
- MathSciNet review: 773994