On KAC’S principle of not feeling the boundary for the kohn laplacian on the heisenberg group

Michael Ruzhansky; Durvudkhan Suragan

doi:10.1090/proc/12792

On KAC’S principle of not feeling the boundary for the kohn laplacian on the heisenberg group

Michael Ruzhansky, Durvudkhan Suragan

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

26 Citations (Scopus)

Abstract

In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac’s "principle of not feeling the boundary". This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.

Original language	English
Pages (from-to)	709-721
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	2
DOIs	https://doi.org/10.1090/proc/12792
Publication status	Published - Feb 1 2016
Externally published	Yes

Keywords

Heisenberg group
Integral boundary conditions
Kohn Laplacian
Newton potential
Sub-Laplacian

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/proc/12792

Fingerprint Dive into the research topics of 'On KAC’S principle of not feeling the boundary for the kohn laplacian on the heisenberg group'. Together they form a unique fingerprint.

Cite this

@article{2580b0e533ec4e0e8225b352d250f634,

title = "On KAC{\textquoteright}S principle of not feeling the boundary for the kohn laplacian on the heisenberg group",

abstract = "In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac{\textquoteright}s {"}principle of not feeling the boundary{"}. This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.",

keywords = "Heisenberg group, Integral boundary conditions, Kohn Laplacian, Newton potential, Sub-Laplacian",

author = "Michael Ruzhansky and Durvudkhan Suragan",

year = "2016",

month = feb,

day = "1",

doi = "10.1090/proc/12792",

language = "English",

volume = "144",

pages = "709--721",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - On KAC’S principle of not feeling the boundary for the kohn laplacian on the heisenberg group

AU - Ruzhansky, Michael

AU - Suragan, Durvudkhan

PY - 2016/2/1

Y1 - 2016/2/1

N2 - In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac’s "principle of not feeling the boundary". This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.

AB - In this note we construct an integral boundary condition for the Kohn Laplacian in a given domain on the Heisenberg group extending to the setting of the Heisenberg group M. Kac’s "principle of not feeling the boundary". This also amounts to finding the trace on smooth surfaces of the Newton potential associated to the Kohn Laplacian. We also obtain similar results for higher powers of the Kohn Laplacian.

KW - Heisenberg group

KW - Integral boundary conditions

KW - Kohn Laplacian

KW - Newton potential

KW - Sub-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=84951335460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951335460&partnerID=8YFLogxK

U2 - 10.1090/proc/12792

DO - 10.1090/proc/12792

M3 - Article

AN - SCOPUS:84951335460

VL - 144

SP - 709

EP - 721

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -