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On a new set of orthogonal polynomials

Franz Hinterleitner (2003)

Archivum Mathematicum

An orthogonal system of polynomials, arising from a second-order ordinary differential equation, is presented.

On almost periodicity defined via non-absolutely convergent integrals

Dariusz Bugajewski, Adam Nawrocki (2025)

Czechoslovak Mathematical Journal

We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.

On certain properties of linear iterative equations

Jean-Claude Ndogmo, Fazal Mahomed (2014)

Open Mathematics

An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained,...

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