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Link of groups and homogeneous Hörmander operators
Author(s):
Alessia
Elisabetta
Kogoj;
Ermanno
Lanconelli
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2019-2030.
MSC (2000):
Primary 35K70, 35H10;
Secondary 43A80, 35H20
Posted:
February 28, 2007
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Abstract:
We study a notion of link of Lie groups suggested by the structure of the partial differential operators of Kolmogorov type. As an application of our link procedure we construct explicit examples of stratified Lie groups, with dimension and step arbitrarily large. We also give a set of examples of hypoelliptic second-order operators which are left translation invariant and homogeneous of degree two on the previous groups.
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Additional Information:
Alessia
Elisabetta
Kogoj
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, IT-40126 Bologna, Italy
Email:
kogoj@dm.unibo.it
Ermanno
Lanconelli
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, IT-40126 Bologna, Italy
Email:
lanconel@dm.unibo.it
DOI:
10.1090/S0002-9939-07-08646-7
PII:
S 0002-9939(07)08646-7
Keywords:
H\"ormander operators,
Kolmogorov operators,
partial differential operators on homogeneous Lie groups.
Received by editor(s):
April 14, 2005
Received by editor(s) in revised form:
January 15, 2006
Posted:
February 28, 2007
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
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