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1
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Degenerate evolution problems and Beta-type operators

100%
Attalienti A., Campiti M.
Studia Mathematica
|
2000
|
tom 140
|
nr 2
117-139
EN
The present paper is concerned with the study of the differential operator Au(x):=α(x)u''(x)+β(x)u'(x) in the space C([0,1)] and of its adjoint Bv(x):=((αv)'(x)-β(x)v(x))' in the space $L^1(0,1)$, where α(x):=x(1-x)/2 (0≤x≤1). A careful analysis of their main properties is carried out in view of some generation results available in [6, 12, 20] and [25]. In addition, we introduce and study two different kinds of Beta-type operators as a generalization of similar operators defined in [18]. Among the corresponding approximation results, we show how they can be used in order to represent explicitly the solutions of the Cauchy problems associated with the operators A and Ã, where à is equal to B up to a suitable bounded additive perturbation.
2
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On Martin Bordemann's proof of the existence of projectively equivariant quantizations

75%
Lecomte P.
Open Mathematics
|
2004
|
tom 2
|
nr 5
793-800
EN
The paper explains the notion of projectively equivariant quantization. It gives a sketch of Martin Bordemann's proof of the existence of projectively equivariant quantization on arbitrary manifolds.
3
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Lie algebraic characterization of manifolds

51%
Grabowski J., Poncin N.
Open Mathematics
|
2004
|
tom 2
|
nr 5
811-825
EN
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the appropriate class of diffeomorphisms of the underlying manifolds.
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