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1
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Connections between Romanovski and other polynomials

100%
Weber H.
Open Mathematics
|
2007
|
tom 5
|
nr 3
581-595
EN
A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.
2
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Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

100%
Weber H.
Open Mathematics
|
2007
|
tom 5
|
nr 2
415-427
EN
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.
3
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The order topology for a von Neumann algebra

51%
Chetcuti E., Hamhalter J., Weber H.
Studia Mathematica
|
2015
|
tom 230
|
nr 2
95-120
EN
The order topology $τ_{o}(P)$ (resp. the sequential order topology $τ_{os}(P)$) on a poset P is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a von Neumann algebra M we consider the following three posets: the self-adjoint part $M_{sa}$, the self-adjoint part of the unit ball $M¹_{sa}$, and the projection lattice P(M). We study the order topology (and the corresponding sequential variant) on these posets, compare the order topology to the other standard locally convex topologies on M, and relate the properties of the order topology to the underlying operator-algebraic structure of M.
4
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κ-compactness, extent and the Lindelöf number in LOTS

51%
Buhagiar D., Chetcuti E., Weber H.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1249-1264
EN
We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.
5
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Nonlinear transformations on spaces of continuous functions

32%
Volkmer H., Weber H.
Studia Mathematica
|
1987
|
tom 86
|
nr 3
221-237
6
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Die atomare Struktur topologischer Boolescher Ringe und s-beschränkter Inhalte

32%
Weber H.
Studia Mathematica
|
1982
|
tom 74
|
nr 1
57-81
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