ATOMIC
WAVELETS
I.V. Brysina,
V.A. Makarichev
The problem of
existence and construction of the atomic wavelet system, which consists of infinitely
differentiable functions with a compact support, is considered. Formulas for
evaluation atomic wavelets are obtained. Examples of applications of atomic
wavelets to approximation of some functions are presented. Compactly supported
solutions of some functional differential equations and their properties are
considered. A new class of atomic functions is introduced. Approximation properties of the linear spaces of finite linear combinations of
translates of the atomic functions are presented.
Key words: wavelet,
functional differential equation, atomic function, atomic wavelet, function
with compact support, infinitely differentiable function, nonstationary
wavelet system.