Application of Nilpotent Approximation and the Orbit Method to the Search of the Diagonal Asymptotics of Sub-Riemannian Heat Kernels

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Application of Nilpotent Approximation and the Orbit Method to the Search of the Diagonal Asymptotics of Sub-Riemannian Heat Kernels. / Kuznetsov, M. V.

In: Siberian Mathematical Journal, Vol. 60, No. 6, 01.11.2019, p. 1051-1074.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{25b60f131783477282cc614a6f7164d1,

title = "Application of Nilpotent Approximation and the Orbit Method to the Search of the Diagonal Asymptotics of Sub-Riemannian Heat Kernels",

abstract = "We propose a general scheme for the search of a fundamental solution to the hypoelliptic diffusion equation in a “sufficiently good” sub-Riemannian manifold and the small-time asymptotics for the solution, which includes the generalized Fourier transform and the orbit method closely related to it, as well as an application of the perturbative method to the nilpotent approximation, and Trotter{\textquoteright}s formula.",

keywords = "nilpotent Lie group, noncommutative harmonic analysis, orbit method, representation theory, sub-Laplacian",

author = "Kuznetsov, {M. V.}",

year = "2019",

month = nov,

day = "1",

doi = "10.1134/S0037446619060132",

language = "English",

volume = "60",

pages = "1051--1074",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "6",

}

RIS

TY - JOUR

T1 - Application of Nilpotent Approximation and the Orbit Method to the Search of the Diagonal Asymptotics of Sub-Riemannian Heat Kernels

AU - Kuznetsov, M. V.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We propose a general scheme for the search of a fundamental solution to the hypoelliptic diffusion equation in a “sufficiently good” sub-Riemannian manifold and the small-time asymptotics for the solution, which includes the generalized Fourier transform and the orbit method closely related to it, as well as an application of the perturbative method to the nilpotent approximation, and Trotter’s formula.

AB - We propose a general scheme for the search of a fundamental solution to the hypoelliptic diffusion equation in a “sufficiently good” sub-Riemannian manifold and the small-time asymptotics for the solution, which includes the generalized Fourier transform and the orbit method closely related to it, as well as an application of the perturbative method to the nilpotent approximation, and Trotter’s formula.

KW - nilpotent Lie group

KW - noncommutative harmonic analysis

KW - orbit method

KW - representation theory

KW - sub-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=85079726485&partnerID=8YFLogxK

U2 - 10.1134/S0037446619060132

DO - 10.1134/S0037446619060132

M3 - Article

AN - SCOPUS:85079726485

VL - 60

SP - 1051

EP - 1074

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -

ID: 23577025