FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
Journal Title: Проблемы анализа-Issues of Analysis - Year 2017, Vol 6, Issue 1
Abstract
We construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour of Fourier coefficients of continuous functions with respect to a localized Haar system. The function f* has fractal structure. We give lower bounds on its smoothness.
Authors and Affiliations
Elena Belkina, Yu. V. Malykhin
Keywords
Related Articles
- EP ID EP225100
- DOI 10.15393/j3.art.2017.3871
- Views 113
- Downloads 0
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle
Let C be the unit circle {z:|z|= 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L2[−1,1] is greater tha...
NECESSARY AND SUFFICIENT CONDITIONS OF (α, β)-ACCESSIBILITY OF DOMAIN IN NONSMOOTH CASE
In [1], [2] (α, β)-accessible domains in C were defined and investigated, and the criterion of (α, β)-accessibility in a smooth case was obtained. (α, β)-accessible domains are starlike, γ-accessible (γ = min{α, β}), and...
ГАРМОНИЧЕСКИЙ АНАЛИЗ ДАНКЛЯ И НЕКОТОРЫЕ ЗАДАЧИ ТЕОРИИ ПРИБЛИЖЕНИЙ ФУНКЦИЙ. II
Using generalized translations of Dunkl we define Nikolskii - Besov type function spaces and obtain their description in terms of the best approximations.
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated...
УСЛОВИЯ ЗВЕЗДООБРАЗНОСТИ ОБЛАСТЕЙ В R^N
Для областей с гладкой границей получен критерий звездообразности области относительно внутренней или граничной точки. В качестве приложения отсюда получаются все известные условия звездообразности биголоморфных отображе...