Hormander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

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Hormander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity. / Ruzhansky, Michael; Turunen, Ville; Wirth, Jens.

julkaisussa: Journal of Fourier Analysis and Applications, Vuosikerta 20, Nro 3, 06.2014, s. 476-499.

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

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Bibtex - Lataa

@article{faa36be22456402182db17201803e5dc,
title = "Hormander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity",
abstract = "In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.",
keywords = "Pseudo-differential operators, compact Lie groups, microlocal analysis, elliptic operators, global hypoellipticity, Leibniz formula",
author = "Michael Ruzhansky and Ville Turunen and Jens Wirth",
year = "2014",
month = "6",
doi = "10.1007/s00041-014-9322-9",
language = "English",
volume = "20",
pages = "476--499",
journal = "Journal of Fourier Analysis and Applications",
issn = "1069-5869",
number = "3",

}

RIS - Lataa

TY - JOUR

T1 - Hormander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

AU - Ruzhansky, Michael

AU - Turunen, Ville

AU - Wirth, Jens

PY - 2014/6

Y1 - 2014/6

N2 - In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.

AB - In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.

KW - Pseudo-differential operators

KW - compact Lie groups

KW - microlocal analysis

KW - elliptic operators

KW - global hypoellipticity

KW - Leibniz formula

U2 - 10.1007/s00041-014-9322-9

DO - 10.1007/s00041-014-9322-9

M3 - Article

VL - 20

SP - 476

EP - 499

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

IS - 3

ER -

ID: 9681860