Zhedanov's algebra and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra.
Koornwinder, Tom H. (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Koornwinder, Tom H. (2008)
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Koornwinder, Tom H. (2007)
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In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties...
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Kulish, Petr, Lyakhovsky, Vladimir (2008)
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Kazimierz Nikodem, Zsolt Páles, Szymon Wąsowicz (1999)
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Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.