Nearly Invariant Subspaces Related to Multiplication Operators in Hilbert Spaces of Analytic Functions

We consider Hilbert spaces of analytic functions defined on an open subset of , stable under the operator M_u of multiplication by some function u. Given a subspace of which is nearly invariant under division by u, we provide a factorization linking each element of to elements of on the inverse image under u of a certain complex disc, for which we give a relatively simple formula. By applying these results to and u(z) = z, we obtain interesting results involving a H²-norm control. In particular, we deduce a factorization for the kernel of Toeplitz operators on Dirichlet spaces. Finally, we give a localization for the problem of extraneous zeros.Submitted: January 18, 2003 Revised: December 20, 2003     

Maximum decay rate for the nonlinear Schrödinger equation

In this paper, we consider global solutions for the following nonlinear Schrödinger equation in with and We show that no nontrivial solution can decay faster than the solutions of the free Schrödinger equation, provided that u(0) lies in the weighted Sobolev space in the energy space, namely or in according to the different cases.     

An Lp-Lq-Version of Morgan’s Theorem for the Dunkl-Bessel Transform

In this paper, we give an L^p-L^q-version of Morgans theorem for the Dunkl-Bessel transform on More precisely, we prove that for all and then for all measurable function f on the conditions and imply f = 0, if and only if where are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004     

Evolution systems and perturbations of generators of strongly continuous groups

Suppose A generates a strongly continuous linear group on a Banach space X and B is a linear operator on X. It is shown that an extension of generates a strongly continuous semigroup if and only if the family of operators has an appropriate evolution system. This produces simple sufficient conditions for an extension of to generate a strongly continuous semigroup, including

Dynamics of Properties of Toeplitz Operators with Radial Symbols

In the case of radial symbols we study the behavior of different properties (boundedness, compactness, spectral properties, etc.) of Toeplitz operators T_a⁽⁾ acting on weighted Bergman spaces over the unit disk , in dependence on , and compare their limit behavior under with corresponding properties of the initial symbol a.     

Large deviations of the steady-state distribution of reflected processes with applications to queueing systems

We consider a Skorohod map which takes paths in to paths which stay in the positive orthant . We let be the domain of definition of . A convex and lower semi-continuous function and a set are given. We are concerned with the calculation of the infimum of the value for t ⩾ 0 and absolutely continuous subject to the conditions and . We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems. This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations of heavily loaded queueing networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Quasiapproximate $(\mathcal{U} + \mathcal{K})$ –Invariants of Essentially Normal Operators

For a class of essentially normal operators, we characterize their norm closures of –orbits. Moreover, we introduce a notion of the quasiapproximate – equivalence of essentially normal operators and determine completely the quasiapproximate –invariants. Finally, we give the canonical forms of essentially normal operators under this quasiapproximate –equivalence.     

Affine congruence by dissection of discs - appropriate groups and optimal dissections

Let be a group of affine transformations of the Euclidean plane . Two topological discs D, are called congruent by dissection with respect to if D can be dissected into a finite number of subdiscs that can be rearranged by maps from to a dissection of E. Our main result says in particular that admits congruence by dissection of any circular disc C with any square S if and only if contains a contractive map and all orbits , , are dense in . In this case any two discs D and E are congruent by dissection with respect to and every disc D is congruent by dissection with n copies of D for every n ≥ 2. Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection. Dedicated to Irmtraud Stephani on the occasion of her 70th birthday     

Subdominant Matroid Ultrametrics

Given a matroid M on the ground set E, the Bergman fan or space of M-ultrametrics, is a polyhedral complex in which arises in several different areas, such as tropical algebraic geometry, dynamical systems, and phylogenetics. Motivated by the phylogenetic situation, we study the following problem: Given a point in we wish to find an M-ultrametric which is closest to it in the -metric. The solution to this problem follows easily from the existence of the subdominant M-ultrametric: a componentwise maximum M-ultrametric which is componentwise smaller than . A procedure for computing it is given, which brings together the points of view of matroid theory and tropical geometry. When the matroid in question is the graphical matroid of the complete graph K_n, the Bergman fan parameterizes the equidistant phylogenetic trees with n leaves. In this case, our results provide a conceptual explanation for Chepoi and Fichets method for computing the tree that most closely matches measured data.Received August 12, 2004     

Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.     

Weak and strong solvability of parabolic variational inequalities in Banach spaces

We consider parabolic variational inequalities having the strong formulation

Varieties Defined by Permutations

We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form . A criterion is given determining whether a cyclic variety is interpretable in . For a permutation without fixed elements, it is stated that a set of primes for which is interpretable in in the lattice is finite. It is also proved that for distinct primes , the Helly number of a type in coincides with dimension of the dual type and equals .     

Compact Differences of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Let be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings and which characterize the compactness of differences of two weighted composition operators on the space . As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.      

On posets with isomorphic interval posets

Let be a partially ordered set, Int the system of all (nonempty) intervals of partially ordered by the set-theoretical inclusion . We are interested in partially ordered sets with Int isomorphic to Int . We are going to show that they correspond to couples of binary relations on A satisfying some conditions. If is a directed partially ordered set, the only with Int isomorphic to Int are corresponding to direct decompositions of ( denotes the dual of . The present results include those presented in the paper [11] by V. Slavík. Systems of intervals, particularly of lattices, have been investigated by many authors, cf. [1]–[11].     

Extension of Locally Defined Indefinite Functions on Ordered Groups

We give a definition of -indefinite function of archimedean type, on an interval of an ordered group with an archimedean point. We say that has the indefinite extension property if every continuous -indefinite function of archimedean type, on an interval of , can be extended to a continuous -indefinite function on the whole group .We show that if a group is semi-archimedean and it has the indefinite extension property, then with the lexicographic order and the product topology has the indefinite extension property. As a corollary it is obtained that the groups and with the lexicographic order and the usual topologies, have the indefinite extension property.To Professor José R. León, for his kind encouragement.Both authors were supported in part by the CDCH of the Univ. Central de Venezuela and by CONICIT grant G-97000668. Both authors were visitors at IVIC during the realization of this paper.Submitted: August 8, 2002 Revised: January 30, 2003