Several wav elets from well known biorthogonal families are shown to be unbounded on every interval. One, in fact, is shown to be infinite at each dyadic rational. Not withstanding these facts, we show how to compute exact values for these wav elets at many points and thus achieve exact pictures for these functions.

We consider an infinite-horizon optimal control problem with the cost functional described either by an integral over an unbounded interval (a Lebesgue integral) or by a limit of integrals (an improper Lebesgue integral). We prove some theorems on the existence of solutions to such problems. The proofs are based on appropriate lower closure theorems and some extensions of Olech’s theorem on the...

Abstract In this paper we prove the existence of solutions for a boundary value nonlinear neutral integrodifferential problem in Rn defined on an unbounded interval. The result is obtained by using the Schaefer fixed point theorem and by using a recent result [4] on compactness of a continuous operator K : BC(I,Rn) → BC(I,Rn); here BC(I,Rn) is the Banach space of continuous functions from the (...

We present an extension of the classical testing semantics for the case when nondeterminism is unbounded. We deene the corresponding may and must preorders in the new framework. As in the bounded setting the may preorder can be characterized by using the set of nite traces of processes. On the contrary, in order to characterize the must preorder is necessary to record some additional informatio...

In this paper, we study the boundedness of pseudo-differential operators with symbols in Sm ρ,δ on the modulation spaces M p,q. We discuss the order m for the boundedness Op(Sm ρ,δ) ⊂ L(M p,q(Rn)) to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space Mp,q with q 6= 2. This unboundedness is still true even if we assume a generalized T...