Details
| Original language | English |
|---|---|
| Pages (from-to) | 188-234 |
| Number of pages | 47 |
| Journal | Advances in mathematics |
| Volume | 271 |
| Publication status | Published - 11 Dec 2014 |
Abstract
We examine a class of Grushin type operators Pk where k∈N0 defined in (1.1). The operators Pk are non-elliptic and degenerate on a sub-manifold of RN+ℓ. Geometrically they arise via a submersion from a sub-Laplace operator on a nilpotent Lie group of step k+1. We explain the geometric framework and prove some analytic properties such as essential self-adjointness. The main purpose of the paper is to give an explicit expression of the fundamental solution of Pk. Our methods rely on an appropriate change of coordinates and involve the theory of Bessel and modified Bessel functions together with Weber's second exponential integral.
Keywords
- Bessel function, Fundamental solution, Grushin type operator, Modified bessel function, Nilpotent lie group, Sub-Laplacian
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Advances in mathematics, Vol. 271, 11.12.2014, p. 188-234.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Fundamental solution of a higher step Grushin type operator
AU - Bauer, Wolfram
AU - Furutani, Kenro
AU - Iwasaki, Chisato
N1 - Publisher Copyright: © 2014 Elsevier Inc. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/12/11
Y1 - 2014/12/11
N2 - We examine a class of Grushin type operators Pk where k∈N0 defined in (1.1). The operators Pk are non-elliptic and degenerate on a sub-manifold of RN+ℓ. Geometrically they arise via a submersion from a sub-Laplace operator on a nilpotent Lie group of step k+1. We explain the geometric framework and prove some analytic properties such as essential self-adjointness. The main purpose of the paper is to give an explicit expression of the fundamental solution of Pk. Our methods rely on an appropriate change of coordinates and involve the theory of Bessel and modified Bessel functions together with Weber's second exponential integral.
AB - We examine a class of Grushin type operators Pk where k∈N0 defined in (1.1). The operators Pk are non-elliptic and degenerate on a sub-manifold of RN+ℓ. Geometrically they arise via a submersion from a sub-Laplace operator on a nilpotent Lie group of step k+1. We explain the geometric framework and prove some analytic properties such as essential self-adjointness. The main purpose of the paper is to give an explicit expression of the fundamental solution of Pk. Our methods rely on an appropriate change of coordinates and involve the theory of Bessel and modified Bessel functions together with Weber's second exponential integral.
KW - Bessel function
KW - Fundamental solution
KW - Grushin type operator
KW - Modified bessel function
KW - Nilpotent lie group
KW - Sub-Laplacian
UR - http://www.scopus.com/inward/record.url?scp=84916910169&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2014.11.017
DO - 10.1016/j.aim.2014.11.017
M3 - Article
AN - SCOPUS:84916910169
VL - 271
SP - 188
EP - 234
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
ER -