Abstract We introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) bounded variation. In our approach we define analogue the partial sums with help Dirichlet kernel using newly defined weighted metric integral. derive error bounds for these approximants. As a consequence, prove that sequence converges pointwisely in Hausdorff values approximated...

let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .

It is well known that sets of finite perimeter can be strictly approximated by smooth sets, while, in general, one cannot hope to approximate an open set Ω of finite perimeter in R strictly from within. In this note we show that, nevertheless, the latter type of approximation is possible under the mild hypothesis that the (n−1)-dimensional Hausdorff measure of the topological boundary ∂Ω equals...

A. We investigate the parameterized complexity of generalisations and variations of the dominating set problem on classes of graphs that are nowhere dense. In particular, we show that the distance-d dominating-set problem, also known as the (k, d)-centres problem, is fixed-parameter tractable on any class that is nowhere dense and closed under induced subgraphs. This generalises known re...