A Cantor-Lebesgue theorem for double trigonometric series
A counterexample in harmonic analysis
A divergent multiple Fourier series of power series type
A later note on the relationships of numerical sequences.
A new criterion for the absolute Riesz summability of the conjugate series of a Fourier series
A note on convergence to infinity of Fourier series
A note on integer translates of a square integrable function on ℝ
We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family , which is equivalent to the weight function being > 0 a.e.
A note on -convergence of the sine and cosine trigonometric series with semi-convex coefficients.
A theorem of Cesari on mulitple Fourier series
A theorem on the absolute Riesz summability factors of a Fourier series
A variation norm Carleson theorem
We strengthen the Carleson-Hunt theorem by proving estimates for the -variation of the partial sum operators for Fourier series and integrals, for . Four appendices are concerned with transference, a variation norm Menshov-Paley-Zygmund theorem, and applications to nonlinear Fourier transforms and ergodic theory.
Absolute convergence of Fourier series of a function of Wiener’s class
Absolute convergence of Fourier series on finite-dimensional groups
Absolute Nörlund summability factors of power series and Fourier series
Four theorems of Ahmad [1] on absolute Nörlund summability factors of power series and Fourier series are proved under weaker conditions.
Absolute Nörlund summability factors of power series and Fourier series
Accelerating the convergence of trigonometric series
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.
Additions to the Telyakovskiĭ's class .
Algebrability of the set of non-convergent Fourier series
We show that, given a set E ⊂ 𝕋 of measure zero, the set of continuous functions whose Fourier series expansion is divergent at any point t ∈ E is dense-algebrable, i.e. there exists an infinite-dimensional, infinitely generated dense subalgebra of 𝓒(𝕋) every non-zero element of which has a Fourier series expansion divergent in E.
An equation with no -periodic solutions.
An estimate of the rate convergence of Cesaro means of Fourier Stieltjes series and its conjugate series