This paper presents a general approach to a multiresolution analysis and wavelet spaces on the interval Our method is based on the Chebyshev transform correspond ing shifts and the discrete cosine transform DCT For the wavelet analysis of given functions e cient decomposition and reconstruction algorithms are proposed using fast DCT algorithms As examples for scaling functions and wavelets poly...

Periodic solutions of certain large-scale systems of ODEs can be computed ee-ciently using a hybrid Newton{Picard scheme, especially in a continuation context. In this paper we describe and analyse how this approach can be extended to the direct computation of period doubling bifurcation points. The Newton{Picard scheme is based on shooting and a splitting of the state space in a low-dimensiona...

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X −→ X such that the set A = {x ∈ X : ||Rx|| → ∞} is non-empty and nowhere dense in X. Moreover, if x ∈ X \ A then some subsequence of (Rx)n=1 converges weakly to x. This answers in the negative a recent conjecture of Prǎjiturǎ. The result can be extended to any Banach s...

In this work, the definition of first and second types multiplicative Chebyshev differential equations is given solutions these are investigated with help power series. Also, properties type polynomials proved. Finally, studies supported numerical examples.

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X −→ X such that the set A = {x ∈ X : ||R(x)|| → ∞} is non-empty and nowhere dense in X . Moreover, if x ∈ X \ A then some subsequence of (R(x)) n=1 converges weakly to x. This answers in the negative a recent conjecture of Prǎjiturǎ. The result can be extended to any Ba...

We establish that if F is a countable field of characteristic p, U is a unitary action of F` on a Hilbert space H , and P is an essential idempotent ultrafilter on F then for every polynomial r : F → F` with r(0) = 0 one has P-limg Ur(g)f = Prf weakly, where Pr is the projection onto the closed subspace Kr = { f ∈ H : {Ur(g)f}g∈F is precompact in the strong topology } . We then derive combinato...

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from unique. However, uniqueness can be reestablished through the introduction of a dynamical time averaging map. The generator of the resulting Contraction Semigroup ...

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.