Page 136 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts

ROXIMATION THEORY AND APPLICATIONS (MS-78)

On derivative sampling using Kantorovich-type sampling operators

Gert Tamberg, gert.tamberg@taltech.ee
Tallinn University of Technology, Estonia
Coauthor: Olga Graf

For f ∈ C(R) the generalized sampling operators are given by (t ∈ R; W > 0)

∞k
(SW f )(t) := f ( )s(W t − k), (1)
W
k=−∞

where s is a certain kernel function, i.e.

s ∈ L1(R), s(u − k) = 1, (u ∈ R).

k∈Z

We show a connection between generalized sampling operators with averaged kernels and gen-
eralized Kantorovich-type sampling operators. Using this connection, we can estimate the order
of approximation of derivatives.

A general method to study the convergence of nonlinear operators in
Orlicz spaces

Luca Zampogni, luca.zampogni@unipg.it

University of Perugia, Italy

Coauthor: Gianluca Vinti

We introduce a general setting in which we define nets of nonlinear operators whose domains
are some set of functions defined in a locally compact topological group G. These nets assume
the form

Twf := z → χw(z − hw(t), Lhw(t)(f ))dµH (t), x > 0,

H

where H is a topological group with (left-invariant) Haar measure µH, (χw)w is a net of Kernels
functions defined on G × R, hw are homeomorphism from H to G and Lhw(t) : L(G) → R are
linear operators.

We analyze the behavior of such nets, and detect the fairest assumption which are needed
for the nets to converge in Orlicz spaces. As a consequence, we give a result of convergence in
a subspace of a Orlicz space.

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