The paper considers the basis and frame properties of the system of weighted exponentials E(g,Z\F ) = {eg(x)}n∈Z\F in L(T), where g ∈ L2(T)\{0} and F ⊂ Z. It is shown that many of the frame properties of E(g,Z\F ) are affected by the cardinalities of F and the behavior of the zeros of g.

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

It has been argued that the solar magnetic cycle consists of two main periodic components: a low-frequency component (Hale’s 22-year cycle) and a high-frequency component (quasi-biennial cycle). The existence of the double magnetic cycle on the Sun is confirmed using Stanford, Mount Wilson and Kitt Peak magnetograph data from 1976 to 1996 (solar cycles 21 and 22). In the frame of the Parker’s d...

The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from Sand BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the ...

The topic of Hamiltonian chaos is a whole course in itself, and we will only touch on a few highlights. For further information see Ott chapter 7, and review papers by Berry [1] and Helleman [2]. The ideal pendulum discussed in chapter 2 is an example of a Hamiltonian system. In many ways this system is typical of the ones taught in elementary courses on mechanics: the orbits are periodic and c...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...