Almost periodic functions and uniform distribution mod 1.
Almost periodic sequences and functions with given values
We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set in a metric space, it is proved the existence of an almost periodic sequence such that and , for all and some which depends on .
Almost periodic solutions with a prescribed spectrum of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Neutral differential equations)
The paper is the extension of the author's previous papers and solves more complicated problems. Almost periodic solutions of a certain type of almost periodic linear or quasilinear systems of neutral differential equations are dealt with.
Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Cauchy integral)
This paper generalizes earlier author's results where the linear and quasilinear equations with constant coefficients were treated. Here the method of limit passages and a fixed-point theorem is used for the linear and quasilinear equations with almost periodic coefficients.
Almost periodic solutions with a prescribed spectrum of systems of linear and quasilinear differential equations with almost periodic coefficients and constant time lag (Fourier transform approach)
This paper is a continuation of my previous paper in Mathematica Bohemica and solves the same problem but by means of another method. It deals with almost periodic solutions of a certain type of almost periodic systems of differential equations.
Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum.
Almost periodicity of some error terms in prime number theory
Almost sure absolute continuity of Bernoulli convolutions
We prove an extension of a result by Peres and Solomyak on almost sure absolute continuity in a class of symmetric Bernoulli convolutions.
Almost-everywhere convergence of Fourier integrals for functions in Sobolev spaces, and an L2-localisation principle.
Almost-periodic solutions in various metrics of higher-order differential equations with a nonlinear restoring term
Almost-periodic solutions in various metrics (Stepanov, Weyl, Besicovitch) of higher-order differential equations with a nonlinear Lipschitz-continuous restoring term are investigated. The main emphasis is focused on a Lipschitz constant which is the same as for uniformly almost-periodic solutions treated in [A1] and much better than those from our investigations for differential systems in [A2], [A3], [AB], [ABL], [AK]. The upper estimates of for -almost-periods of solutions and their derivatives...
Alternative characterisations of Lorentz-Karamata spaces
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
Alternative orthogonal polynomials and quadratures.
An abstract version of Herz' imbedding theorem
An Addition Theorem for Some q-Hahn Polynomials.
An algebra of integral operators.
An Algebraic Approach to Discrete Dilations. Application to Discrete Wavelet Transforms.
An algebraic construction of discrete wavelet transforms
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
An algorithm for nonharmonic signal analysis using Dirichlet series on convex polygons.
An Almost Orthogonal Radial Wavelet Expansion for Radial Distributions.
An analogue of Gutzmer's formula for Hermite expansions
We prove an analogue of Gutzmer's formula for Hermite expansions. As a consequence we obtain a new proof of a characterisation of the image of L²(ℝⁿ) under the Hermite semigroup. We also obtain some new orthogonality relations for complexified Hermite functions.