Restricted Mean Values And Harmonic Functions

John R. Baxter

doi:10.1090/S0002-9947-1972-0293112-4

Restricted Mean Values And Harmonic Functions

John R. Baxter

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

13 Scopus citations

Abstract

A function h defined on a region R in Rⁿ will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.

Original language	English (US)
Pages (from-to)	451-463
Number of pages	13
Journal	Transactions of the American Mathematical Society
Volume	167
DOIs	https://doi.org/10.1090/S0002-9947-1972-0293112-4
State	Published - May 1972
Externally published	Yes

Publisher link

10.1090/S0002-9947-1972-0293112-4

Find It

Find It at U of M Libraries

Cite this

@article{663273ae7112493caffbb3b652e3583c,

title = "Restricted Mean Values And Harmonic Functions",

abstract = "A function h defined on a region R in Rn will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.",

author = "Baxter, \{John R.\}",

year = "1972",

month = may,

doi = "10.1090/S0002-9947-1972-0293112-4",

language = "English (US)",

volume = "167",

pages = "451--463",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Restricted Mean Values And Harmonic Functions

AU - Baxter, John R.

PY - 1972/5

Y1 - 1972/5

N2 - A function h defined on a region R in Rn will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.

AB - A function h defined on a region R in Rn will be said to possess a restricted mean value property if the value of the function at each point is equal to the mean value of the function over one open ball in R, with centre at that point. It is proved here that this restricted mean value property implies h is harmonic under certain conditions.

UR - https://www.scopus.com/pages/publications/0037906754

UR - https://www.scopus.com/pages/publications/0037906754#tab=citedBy

U2 - 10.1090/S0002-9947-1972-0293112-4

DO - 10.1090/S0002-9947-1972-0293112-4

M3 - Article

AN - SCOPUS:0037906754

SN - 0002-9947

VL - 167

SP - 451

EP - 463

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -

Restricted Mean Values And Harmonic Functions

Abstract

Publisher link

Find It

Other files and links

Fingerprint

Cite this