* 0-7803-7952-7/03/$17.00  2003 IEEE. Abstract Uniform ultimate boundedness of a new class of switched linear systems is considered. A switched linear system in this class consists of m subsystems, and none of the individual subsystems need to be stabilizable. The switched linear system is shown to be uniformly ultimately bounded for any pre-given bound if the combination of controllable compo...

Abstract. We consider a Lagrange–Hermite polynomial, interpolating a function at the Jacobi zeros and, with its first (r−1) derivatives, at the points ±1. We give necessary and sufficient conditions on the weights for the uniform boundedness of the related operator in certain suitable weighted L-spaces, 1 < p < ∞, proving a Marcinkiewicz inequality involving the derivative of the polynomial at ...

A given Datalog program is bounded if its depth of recursion is independent of the input database. Deciding boundedness is a basic task for the analysis of database logic programs. The undecidability of Datalog boundedness was rst demonstrated by Gaifman et al. We introduce new techniques for proving the undecidability of various kinds of boundedness, which allow us to considerably strengthen t...

We consider a generic sequence of matrices (the nonnormal case is of interest) showing a proper cluster at zero in the sense of the singular values. By a direct use of the notion of majorizations, we show that the uniform spectral boundedness is sufficient for the proper clustering at zero of the eigenvalues: if the assumption of boundedness is removed, then we can construct sequences of matric...

In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, the...

Using the idea of the optimal decomposition developed in recent papers [EK2] by the same authors and in [CUK] we study the boundedness of the operator Tg(x) = ∫ 1 x g(u) du/u, x ∈ (0, 1), and its logarithmic variant between Lorentz spaces and exponential Orlicz and Lorentz-Orlicz spaces. These operators are naturally linked with Moser’s lemma, O’Neil’s convolution inequality, and estimates for ...

In this paper we investigate the relation between discrete and continuous operators. More precisely, we investigate the properties of the semigroup generated by A, and the sequence Ad , n ∈ N, where Ad = (I +A)(I −A)−1. We show that if A and A−1 generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger...

SPACES, AND NORMS OF WEIGHTED COMPOSITION OPERATORS MICHAEL T. JURY Abstract. We prove that the norm of a weighted composition operator on the Hardy space H2 of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on H2, and ...

We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula φ(X,x) that is positive in X, it is decidable whether the fixed-point recursion based on φ is spurious over the class of all trees in the sense that there is some uniform finite bound for the number of iterations φ takes ...

In this paper, we propose an algorithm to solve the Decisional Diffie-Hellman problem over finite fields, whose time complexity depends on the effective bound in the Uniform Boundedness Theorem (UBT). We show that curves which are defined over a number field of small degree but have a large torsion group over the number field have considerable cryptographic significance. If those curves exist a...