A class of solvable non-homogeneous differential operators on the Heisenberg group

Detlef Müller, and Zhenqiu Zhang. "A class of solvable non-homogeneous differential operators on the Heisenberg group." Studia Mathematica 148.1 (2001): 87-96. <http://eudml.org/doc/285313>.

@article{DetlefMüller2001,
abstract = {In [8], we studied the problem of local solvability of complex coefficient second order left-invariant differential operators on the Heisenberg group ℍₙ, whose principal parts are "positive combinations of generalized and degenerate generalized sub-Laplacians", and which are homogeneous under the Heisenberg dilations. In this note, we shall consider the same class of operators, but in the presence of left invariant lower order terms, and shall discuss local solvability for these operators in a complete way. Previously known methods to study such non-homogeneous operators, as in [9] or [6], do not apply to these operators, and it is the main purpose of this article to introduce a new method, which should be applicable also in much wider settings.},
author = {Detlef Müller, Zhenqiu Zhang},
journal = {Studia Mathematica},
keywords = {local solvability},
language = {eng},
number = {1},
pages = {87-96},
title = {A class of solvable non-homogeneous differential operators on the Heisenberg group},
url = {http://eudml.org/doc/285313},
volume = {148},
year = {2001},
}

TY - JOUR
AU - Detlef Müller
AU - Zhenqiu Zhang
TI - A class of solvable non-homogeneous differential operators on the Heisenberg group
JO - Studia Mathematica
PY - 2001
VL - 148
IS - 1
SP - 87
EP - 96
AB - In [8], we studied the problem of local solvability of complex coefficient second order left-invariant differential operators on the Heisenberg group ℍₙ, whose principal parts are "positive combinations of generalized and degenerate generalized sub-Laplacians", and which are homogeneous under the Heisenberg dilations. In this note, we shall consider the same class of operators, but in the presence of left invariant lower order terms, and shall discuss local solvability for these operators in a complete way. Previously known methods to study such non-homogeneous operators, as in [9] or [6], do not apply to these operators, and it is the main purpose of this article to introduce a new method, which should be applicable also in much wider settings.
LA - eng
KW - local solvability
UR - http://eudml.org/doc/285313
ER -