Journal of Mathematical Extension
Volume:1 Issue: 2, Spring 2007

In this paper we investigate the relation between universal interpolating sequence and the approximate point spectrum of the adjoint multiplication operator acting on the Hilbert spaces of formal power series.

By a brief review on the applications of wavelets in solving optimal control problems, a multiresolution analysis for two dimensional Sobolev spaces and the square spline wavelets are considered. Regarding the density and approximation properties of these wavelets, for the first time, they are employed for solving optimal control problems by embedding method. Existence and the determination way for the solution are also discussed. Finally, the abilities of the new approach are explained by a numerical example and some comparisons.

Let C(K, A) denote the space of all continuous Avalued functions on the compact Hausdorff space K, where A is a commutative Banach algebra. In this paper we show that the maximal ideal space of C(K, A) can be identified with K × M, where M denotes the maximal ideal space of A

. A topological space is said to be almost regular closed Lindeloff (=ARC-Lindeloff) if every cover by regular closed sets has a countable subfamily whose union is dense. In this paper we investigate properties of ARC-Lindeloff. In addition, several example will be provided to illustrate our results.

Let {β(n)}∞ n=−∞ be a sequence of positive numbers such that β(0) = 1 and let 1 < p < ∞. We consider the space of all formal Laurent series f(z) = P∞ n=−∞ ˆf(n)z n such that X∞ n=−∞ | ˆf(n)| pβ(n) p < ∞. We investigate the supercyclicity with respect to a sequence on the Banach spaces of formal Laurent series.

We obtain decay estimates of the energy of solutions to a compactly system of wave equations with a nonlinear boundary dissipation which is weak asut tends to infinity

The aperiodic autocorrelations of those polynomials having coefficients on the unit circle has been useful in telecommunication theory. In this paper we first introduce one such polynomial type and then present a simple relation on its autocorrelations.

Hereditary, directed subsets of a group and a semigroup and some of their properties are discussed. A class of relations in terms of the range projections of a partial representation of a discrete group is introduced. It is shown that the spectrum of these relations is homeomorphic to the set of all characters of the diagonal subalgebra of the Toeplitz algebra.