Strong summability of Ciesielski-Fourier series
A strong summability result is proved for the Ciesielski-Fourier series of integrable functions. It is also shown that the strong maximal operator is of weak type (1,1).
Structure of Fourier exponents of almost periodic functions and periodicity of almost periodic functions
The paper deals with almost periodic functions which are limits of sequences of continuous periodic functions, and determines the structure of their Fourier exponents and their ranges. It is shown that the class of continuous periodic functions is not densely distributed in the space .
Structure of the Hardy operator related to Laguerre polynomials and the Euler differential equation.
We present a direct proof of a known result that the Hardy operator Hf(x) = 1/x ∫0x f(t) dt in the space L2 = L2(0, ∞) can be written as H = I - U, where U is a shift operator (Uen = en+1, n ∈ Z) for some orthonormal basis {en}. The basis {en} is constructed by using classical Laguerre polynomials. We also explain connections with the Euler differential equation of the first order y' - 1/x y = g and point out some generalizations to the case with weighted Lw2(a, b) spaces.
Subalgebras to a Wiener type algebra of pseudo-differential operators
We study general continuity properties for an increasing family of Banach spaces of classes for pseudo-differential symbols, where was introduced by J. Sjöstrand in 1993. We prove that the operators in are Schatten-von Neumann operators of order on . We prove also that and , provided . If instead , then . By modifying the definition of the -spaces, one also obtains symbol classes related to the spaces.
Subrings in trigonometric polynomial rings.
Subspace Weyl-Heisenberg Frames.
Subsystems of the Schauder system whose orthonormalizations are Schauder bases for
Sucesiones de polinomios ortogonales estrictamente γ-típicas.
Sufficient conditions for functions to form Riesz bases in and applications to nonlinear boundary-value problems.
Sufficient Conditions for One-Sided Operators.
Sufficient conditions for the spectrality of self-affine measures with prime determinant
Let be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.
Suite de Rudin-Shapiro et modèle d'Ising
Suites lacunaires de Sidon, ensembles propres et points exceptionnels
Les ensembles “propres” pour une suite de Sidon sont caractérisés par une propriété de convergence des séries lacunaires à spectre dans la suite.
Sulle distribuzioni vettoriali di una variabile debolmente quasi periodiche
Sull'integrazione delle distribuzioni quasi periodiche di una variabile
Summability and integrability of Vilenkin series.
Summability estimates of double Vilenkin-Fourier series.
Summability of derived multiple Fourier series related to slowly oscillating functions with remainder term
Summability of Fourier series with respect to the Walsh-Paley system.
Summability of generalized Fourier series and their conjugate series