Fundamental solution of a higher step Grushin type operator

Autor:	Chisato Iwasaki, Wolfram Bauer, Kenro Furutani
Rok vydání:	2015
Předmět:	Pure mathematics Bessel process General Mathematics Mathematical analysis Lie group Exponential integral symbols.namesake Nilpotent Operator (computer programming) Bessel polynomials symbols Fundamental solution Bessel function Mathematics
Zdroj:	Advances in Mathematics. 271:188-234
ISSN:	0001-8708
DOI:	10.1016/j.aim.2014.11.017
Popis:	We examine a class of Grushin type operators P k where k ∈ N 0 defined in (1.1). The operators P k are non-elliptic and degenerate on a sub-manifold of R N + 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 P k . 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d75b61f7c360a61ea21aede8bbc9d2e5 https://doi.org/10.1016/j.aim.2014.11.017 Zobrazit plný text záznamu Full Text from ScienceDirect