The purpose of this article is to investigate the traces of weak solutions of a linear elliptic equation. In particular, we obtain a sufficient condition for a solution belonging to the Sobolev space to have an L2-trace on the boundar.

In this paper we study nonuniform dichotomy concepts of linear evolutionary processes which are defined in a general Banach space and whose norms can increase no faster than an exponential. Connections between the dichotomy concepts and (B, D) admissibility properties are established. These connections have been partially accomplished in an earlier paper by the authors for the case when the process was a semigroup of class C0 and (B, D) = [(Lp, Lq).

A one-parameter group on evolution space which permutes the classical trajectories of a Lagrangian system is called a dynamical symmetry. Following a review of the modern approach to the “symmetry-conservation law” duality an attempt is made to classify such invariance groups according to the induced transformation of the Cartan form. This attempt is fairly successful inasmuch as the important cases of Lie, Noether and Cartan symmetries can be distinguished. The theory is illustrated with a presentation of results for the classical Kepler problem.

The aim of this note is to prove a theorem on the pointwise degree of approximation of continuously differentiable functions by positive linear operators. As can be seen from the applications to Bernstein and Hermite-Fejér operators, our inequality yields better constants and sometimes even a higher degree of approximation than the known general results.

This paper is devoted to duscussion of some functional equations obtained in the theory of delayed differential equations. By means of the Laplace transform distribution solutions of the considered equations are constructed.

In this article we use real methods to study the Dirichlet and the boundary value problems of an annulus. Then we establish various properties of real Hardy spaces on the annulus, and give some applications.

In this note we give some negative results concerning the question of whether certain integrable functions on the unit circle with mean value zero are expressible as finite sums of differences g – gα of integrable functions g, where gα denotes the translate of g by α.

A Banach algebra A with radical R is said to have property (S) if the natural mapping from the algebraic tensor product A ⊗ A onto A2 is open, when A ⊗ A is given the protective norm. The purpose of this note is to provide a counterexample to Zinde's claim that when A is commutative and R is one dimensional the fulfillment of property (S) in A implies its fulfillment in the quotient algebra A/R.

Let (ωi, σi, μi.) be two positive finite measure spaces, V a non-zero Hilbert space, and 1 ≤ p < ∞, p # 2. In this article it is shown that each surjective linear isometry between the Bochner spaces induces a Boolean isomorphism between the measure algebras , thus generalizing a result of Cambern's for separable Hilbert spaces.

This Banach–Stone type theorem is achieved via a description of the Lp-structure of .

Let R be a ring with Krull dimension α and let τα be defined on a module MR by . Equivalent conditions for τα to be a torsion radical are given. The relationship between τα-criticals and α-criticals is also explored.

In this paper, we consider an optimal control problem involving second-order hyperbolic systems with boundary controls. Necessary and sufficient conditions are derived and a result on the existence of optimal controls is obtained. Also, a computational algorithm which generated minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated.