Search results for "010103 numerical & computational mathematics"
showing 10 items of 260 documents
Standard polynomials and matrices with superinvolutions
2016
Abstract Let M n ( F ) be the algebra of n × n matrices over a field F of characteristic zero. The superinvolutions ⁎ on M n ( F ) were classified by Racine in [12] . They are of two types, the transpose and the orthosymplectic superinvolution. This paper is devoted to the study of ⁎-polynomial identities satisfied by M n ( F ) . The goal is twofold. On one hand, we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew-symmetric matrices for both types of superinvolutions. On the other, in case of M 2 ( F ) , we find generators of the ideal of ⁎-identities and we compute the corresponding sequences of cocharacters and codimensions.
Convex and expansive liftings close to two-isometries and power bounded operators
2021
Abstract In the context of Hilbert space operators, there is a strong relationship between convex and expansive operators and 2-isometries. In this paper, we investigate the bounded linear operators T on a Hilbert space H which have a 2-isometric lifting S on a Hilbert space K containing H as a closed subspace invariant for S ⁎ S . This last property holds in particular when S | K ⊖ H is an isometry. We relate such 2-isometric liftings S by some convex, concave or expansive liftings of the same type as S. We also examine some power bounded operators with such liftings, as well as an intermediate expansive lifting associated with T on the space H ⊕ l + 2 ( H ) . The latter notion is used to …
An asymptotic holomorphic boundary problem on arbitrary open sets in Riemann surfaces
2020
Abstract We show that if U is an arbitrary open subset of a Riemann surface and φ an arbitrary continuous function on the boundary ∂ U , then there exists a holomorphic function φ ˜ on U such that, for every p ∈ ∂ U , φ ˜ ( x ) → φ ( p ) , as x → p outside a set of density 0 at p relative to U . These “solutions to a boundary problem” are not unique. In fact they can be required to have interpolating properties and also to assume all complex values near every boundary point. Our result is new even for the unit disc.
Operators intertwining with isometries and Brownian parts of 2-isometries
2016
Abstract For two operators A and T ( A ≥ 0 ) on a Hilbert space H satisfying T ⁎ A T = A and the A-regularity condition A T = A 1 / 2 T A 1 / 2 we study the subspace N ( A − A 2 ) in connection with N ( A T − T A ) , for T belonging to different classes. Our results generalize those due to C. Kubrusly concerning the case when T is a contraction and A = S T is the asymptotic limit of T. Also, the particular case of a 2-isometry in the sense of S. Richter as well as J. Agler and M. Stankus is considered. For such operators, under the same regularity condition we completely describe the reducing Brownian unitary and isometric parts, as well as the invariant Brownian isometric part. Some exampl…
Characterization of greedy bases in Banach spaces
2017
Abstract We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants.
The exponent for superalgebras with superinvolution
2018
Abstract Let A be a superalgebra with superinvolution over a field of characteristic zero and let c n ⁎ ( A ) , n = 1 , 2 , … , be its sequence of ⁎-codimensions. In [6] it was proved that such a sequence is exponentially bounded. In this paper we capture this exponential growth for finitely generated superalgebras with superinvolution A over an algebraically closed field of characteristic zero. We shall prove that lim n → ∞ c n ⁎ ( A ) n exists and it is an integer, denoted exp ⁎ ( A ) and called ⁎-exponent of A. Moreover, we shall characterize finitely generated superalgebras with superinvolution according to their ⁎-exponent.
Guaranteed lower bounds for cost functionals of time-periodic parabolic optimization problems
2019
In this paper, a new technique is shown for deriving computable, guaranteed lower bounds of functional type (minorants) for two different cost functionals subject to a parabolic time-periodic boundary value problem. Together with previous results on upper bounds (majorants) for one of the cost functionals, both minorants and majorants lead to two-sided estimates of functional type for the optimal control problem. Both upper and lower bounds are derived for the second new cost functional subject to the same parabolic PDE-constraints, but where the target is a desired gradient. The time-periodic optimal control problems are discretized by the multiharmonic finite element method leading to lar…
Comparison of Numerical Methods in the Contrast Imaging Problem in NMR
2013
International audience; In this article, the contrast imaging problem in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. A first synthesis of locally optimal solutions is given in the single-input case using geometric methods based on Pontryagin's maximum principle. We then compare these results using direct methods and a moment-based approach, and make a first step towards global optimality. Finally, some preliminary results are given in the bi-input case.
On the local and semilocal convergence of a parameterized multi-step Newton method
2020
Abstract This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive.
SPECIAL SPLINES OF HYPERBOLIC TYPE FOR THE SOLUTIONS OF HEAT AND MASS TRANSFER 3-D PROBLEMS IN POROUS MULTI-LAYERED AXIAL SYMMETRY DOMAIN
2017
In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the cons…