On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups
Jacek Dziubański, Andrzej Hulanicki (1989)
Studia Mathematica
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Jacek Dziubański, Andrzej Hulanicki (1989)
Studia Mathematica
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Andrzej Hulanicki, Joe Jenkins (1984)
Studia Mathematica
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Jacek Dziubański (1998)
Colloquium Mathematicae
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Nick Dungey, A. ter Elst, Derek Robinson (1999)
Colloquium Mathematicae
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We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel...
Sundaram Thangavelu (1994)
Revista Matemática Iberoamericana
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It is an interesting open problem to establish Paley-Wiener theorems for general nilpotent Lie groups. The aim of this paper is to prove one such theorem for step two nilpotent Lie groups which is analogous to the Paley-Wiener theorem for the Heisenberg group proved in [4].
Linda P. Rothschild (1983)
Journées équations aux dérivées partielles
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José María Ancochea Bermúdez, Otto Rutwig Campoamor (2002)
Revista Matemática Complutense
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In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra L are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Q, which only exists in even dimension as a consequence of the centralizer property....
V. Shul'man (1994)
Banach Center Publications
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We discuss some results and problems connected with estimation of spectra of operators (or elements of general Banach algebras) which are expressed as polynomials in several operators, noncommuting but satisfying weaker conditions of commutativity type (for example, generating a nilpotent Lie algebra). These results have applications in the theory of invariant subspaces; in fact, such applications were the motivation for consideration of spectral problems. More or less detailed proofs...
Mihai Sabac (1996)
Collectanea Mathematica
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In what follows we shall describe, in terms of some commutation properties, a method which gives nilpotent elements. Using this method we shall describe the irreducibility for Lie algebras which have Levi-Malçev decomposition property.
C. Miers (1987)
Studia Mathematica
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