Displaying similar documents to “The heat kernel on Lie groups.”

Spectral multipliers on metabelian groups.

Waldemar Hebisch (2000)

Revista Matemática Iberoamericana

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Let G be a Lie group, Xj right invariant vector fields on G, which generate (as a Lie algebra) the Lie algebra of G, L = -Σ Xj 2. (...) In this paper we consider L1(G) boundedness of F(L) for (some) metabelian G and a distinguished L on G. Of the main interest is that the group is of exponential growth, and possibly higher rank. Previously positive results about higher...

Homogeneous Carnot groups related to sets of vector fields

Andrea Bonfiglioli (2004)

Bollettino dell'Unione Matematica Italiana

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In this paper, we are concerned with the following problem: given a set of smooth vector fields X 1 , … , X m on R N , we ask whether there exists a homogeneous Carnot group G = ( R N , ∘ , δ λ ) such that ∑ i X i 2 is a sub-Laplacian on G . We find necessary and sufficient conditions on the given vector fields in order to give a positive answer to the question. Moreover, we explicitly construct the group law i as above, providing direct proofs. Our main tool is a suitable version of the Campbell-Hausdorff formula. Finally, we...

Some estimates concerning the Zeeman effect

Wiesław Cupała (1993)

Studia Mathematica

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The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.

On rates of propagation for Burgers’ equation

William Alan Day, Giuseppe Saccomandi (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We give asymptotic formulae for the propagation of an initial disturbance of the Burgers’ equation.