In linear algebra, functional analysis and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to all vectors in a vector space, other than the zero vector. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors. A simple example is the 2-dimensional Euclidean space R 2 equipped with the Euclidean norm. Elements in...

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex ...

We study the stability in the H1-seminorm of the L2-projection onto finite element spaces in the case of nonuniform but shape regular meshes in two and three dimensions and prove, in particular, stability for conforming triangular elements up to order twelve and conforming tetrahedral elements up to order seven.

We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities in the log-concave setting and discuss some examples. 2010 Mathematics Subject Classification. Primary 94A17; Secondary 52A40, 60E15.

In an earlier paper [SIAM J. Matrix Anal. Appl. vol. 30 (2008), 925–938] we gave sufficient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving linear systems whose coefficient matrix is Hermitian and positive semidefinite. In this paper we show in which cases these conditions are also necessary, and show that they are not necessary in others.

In this paper Tikhonov regularization for nonlinear illposed problems is investigated. The regularization term is characterized by a closed linear operator, permitting seminorm regularization in applications. Results for existence, stability, convergence and convergence rates of the solution of the regularized problem in terms of the noise level are given. An illustrating example involving para...

We examine a cell-vertex finite volume method which is applied to a model parabolic convection-diffusion problem. By using techniques from finite element analysis, local errors away from all layers are obtained in a seminorm that is related to, but weaker than, the L2 norm.

We show that the minimal discrepancy of a point set in d-dimensional unit cube with respect to BMO seminorm suffers from curse dimensionality.

Abstract We prove residual-type a posteriori error estimates in the maximum norm for linear scalar elliptic convection–diffusion problem that may be singularly perturbed. Similar analysis energy by Verfürth indicates dual of convective derivative must added to natural order residual estimator reliable and efficient. show situation is similar norm. In particular, we define mesh-dependent weighte...