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Accelerating the convergence of trigonometric series

Anry Nersessian, Arnak Poghosyan (2006)

Open Mathematics

A nonlinear method of accelerating both the convergence of Fourier series and trigonometric interpolation is investigated. Asymptotic estimates of errors are derived for smooth functions. Numerical results are represented and discussed.

Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's (Ap) condition.

Yurii I. Lyubarskii, Kristian Seip (1997)

Revista Matemática Iberoamericana

We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 < p < ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...

Exact Kronecker constants of Hadamard sets

Kathryn E. Hare, L. Thomas Ramsey (2013)

Colloquium Mathematicae

A set S of integers is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant, κ(S). The angular Kronecker constant is the unique real number α(S) ∈ [0,1/2] such that κ(S) = |exp(2πiα(S)) - 1|. We show that for integers m > 1 and d ≥ 1, α 1 , m , . . . , m d - 1 = ( m d - 1 - 1 ) / ( 2 ( m d - 1 ) ) and α1,m,m²,... = 1/(2m).

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