We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous estimates in terms of the Euclidean norm. For example, one can use the new approach to get separate error estimates for each action coordinate. An application...

The notion of (unbounded) C∗-seminorms plays a relevant role in the representation theory of ∗-algebras and partial ∗-algebras. A rather complete analysis of the case of ∗-algebras has given rise to a series of interesting concepts like that of semifinite C∗seminorm and spectral C∗-seminorm that give information on the properties of ∗-representations of the given ∗-algebra A and also on the str...

We study the problem of predicting the labelling of a graph. The graph is given and a trial sequence of (vertex,label) pairs is then incrementally revealed to the learner. On each trial a vertex is queried and the learner predicts a boolean label. The true label is then returned. The learner’s goal is to minimise mistaken predictions. We propose minimum p-seminorm interpolation to solve this pr...

Throughout H(U,S) will be used for Γ(U,S) to emphasize the cohomological approach we are taking. First it might be a good idea to recall what a Fréchet space is. A seminorm is an object satisfying all of the norm axioms except for the requirement to have a nonzero kernel. A Fréchet space is a vector space F together with a sequence of seminorms {pn} on F such that (i) if pn(f) = 0 for all n, th...

We show how to obtain continuity in the BV(D.)-seminorm of the L -projection of us BV(íí) into a large class of finite element spaces.

We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator...

Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using...

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that this isomorphism is isometric with respect to the `1-seminorm on singular ho...