The integrability class of the sine transform of a monotonic function
The localization principle for double Fourier series
The Muckenhoupt class A₁(R)
It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.
The multiplication functions of Kučera
The Paley-Wiener-Levinson theorem revisited.
The Poisson summation formula.
The RCWA method - A case study with open questions and perspectives of algebraic computations.
The regularity properties on the real line
The remainder term in Fourier series and its relationship with the Basel problem.
The restriction algebra A(...) for curves ...R...
The Schrödinger density and the Talbot effect
We study the local properties of the time-dependent probability density function for the free quantum particle in a box, i.e. the squared magnitude of the solution of the Cauchy initial value problem for the Schrödinger equation with zero potential, and the periodic initial data. √δ-families of initial functions are considered whose squared magnitudes approximate the periodic Dirac δ-function. The focus is on the set of rectilinear domains where the density has a special character, in particular,...
The size of multipliers
The sizes of the classes of -sets
The class of -sets forms an important subclass of the class of sets of uniqueness for trigonometric series. We investigate the size of this class which is reflected by the family of measures (called polar) annihilating all sets from the class. The main aim of this paper is to answer in the negative a question stated by Lyons, whether the polars of the classes of -sets are the same for all N ∈ ℕ. To prove our result we also present a new description of -sets.
The solvability conditions of the infinite trigonometric moment problem with gaps
The space of multipliers into
The spectral decomposition of weighted shifts and the condition
The Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized for the ergodic Hilbert transform in the case of a one-parameter flow of measure-preserving transformations on a σ-finite measure space.
The structure of quasiasymptotics of Schwartz distributions
In this article complete characterizations of the quasiasymptotic behavior of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to quasiasymptotics of degree -1. It is shown how the structural theorem can be used to study Cesàro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed. A condition for test functions in bigger spaces...
The structure of the -ideal of -porous sets
We show a general method of construction of non--porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non--porous Suslin subset of a topologically complete metric space contains a non--porous closed subset. We show also a sufficient condition, which gives that a certain system of compact sets contains a non--porous element. Namely, if we denote the space of all compact subsets of a compact metric space with the Vietoris topology...
The support of functions and distributions with a spectral gap.