On Bernstein-Euler-Jacobi Operators

In the doctoral dissertation “On Bernstein-Euler-Jacobi Operators” we deal with composition of positive linear operators. Many operators arising in the theory of positive linear operators are compositions of other mappings of this type. Among the most common building blocks we find the classical Bernstein operator and the (Euler-Jacobi) Beta-type operators of various kinds. The purpose of this research is to use these building blocks to provide an overview of the various operators that fit into this pattern and thus to emphasize the importance of understanding the singular pieces that form the composition. To better illustrate this we took one of the less studied operators of this class, namely Păltănea’s operator, and looked closely at its properties and at the way it relates to the properties of the operators that compose it.

Die Arbeit "On Bernstein-Euler-Jacobi Operators" befasst sich mit der Komposition spezieller positiver linearer Operatoren (PLO). Viele Operatoren, die in der entsprechenden Theorie untersucht werden, sind Zusammensetzungen von anderen Abbildungen diesen Typs. Diesem Aspekt wurde in der Vergangenheit jedoch wenig Aufmerksamkeit geschenkt. Er wird am Beispiel einer speziellen Klasse von PLO in der vorliegenden Arbeit systematisch untersucht.


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Stanila, E.D., 2014. On Bernstein-Euler-Jacobi Operators.
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