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Shifted model spaces and their orthogonal decompositions

Câmara M. Cristina, Kliś-Garlicka Kamila, Ptak Marek

Opuscula Mathematica

2024

Vol. 44, no. 3

341--357

We generalize certain well known orthogonal decompositions of model spaces and obtain similar decompositions for the wider class of shifted model spaces, allowing us to establish conditions for near invariance of the latter with respect to certain operators which include, as a particular case, the backward shift S*. In doing so, we illustrate the usefulness of obtaining appropriate decompositions and, in connection with this, we prove some results on model spaces which are of independent interest. We show moreover how the invariance properties of the kernel of an operator T, with respect to another operator, follow from certain commutation relations between the two operators involved.

Quantitative approximation by shift invariant multivariate sublinear-Choquet operators

Anastassiou G. A.

Journal of Applied Analysis

2018

Vol. 24, nr 2

115--126

A very general multivariate positive sublinear Choquet integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it, sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized operators are presented fulfilling all the above properties; the higher order of multivariate approximation of these operators is also studied.