Trigonometric Polynomial Approximation in the L1-Form.
Trigonometric series with gaps
Trigonometric series with -monotone coefficients in spaces with mixed quasinorm.
Trigonometrie Approximation with Exponential Error Orders. I. Construction of Asymptotically Optimal Processes; Generalized de la Vallée Poussin Sums.
Trigonometrische Reihen über multiplikativen Zahlenmengen.
Two complete and minimal systems associated with the zeros of the Riemann zeta function
We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the “dual Poisson formula” of Duffin-Weinberger (also named by us co-Poisson formula), and the “Sonine spaces” of entire functions defined and studied by de Branges. We determine in which (extended) Sonine spaces the zeros define a complete, or minimal, system. We obtain some general results dealing with the distribution of the zeros of the de-Branges-Sonine entire functions. We...
Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
Two examples of subspaces in spanned by characters of finite order
By a Fourier multiplier technique on Cantor-like Abelian groups with characters of finite order, the norms from L² into of certain embeddings of character sums are computed. It turns out that the orders of the characters are immaterial as soon as they are at least four.
Two problems related to the non-vanishing of
We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or , where denotes the “centered” fractional part of . These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet -functions at .
Two random constructions inside lacunary sets
We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is for all but is not a Rosenthal set. This holds also for the sequence of primes.
Two weighted estimates for oscillating kernels I