A proof of bernsteins theorem on regularly monotonicf unctions

J. A.M. McHugh

doi:10.1090/S0002-9939-1975-0354974-3

A proof of bernsteins theorem on regularly monotonicf unctions

J. A.M. McHugh

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

1 Scopus citations

Abstract

A function is called "regularly monotonie" if it is of class C^∞ and each derivative is of a fixed sign (which may depend on the order of the derivative). We present a short proof of Bernstein's theorem on the analyticity of such functions.

Original language	English (US)
Pages (from-to)	358-360
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	47
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1975-0354974-3
State	Published - Feb 1975
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Analyticity
C-infinity functions
Regularly monotonie functions

Access to Document

10.1090/S0002-9939-1975-0354974-3

Cite this

@article{8585d51e80da4922bb63c2b79d8d5e3c,

title = "A proof of bernsteins theorem on regularly monotonicf unctions",

abstract = "A function is called {"}regularly monotonie{"} if it is of class C∞ and each derivative is of a fixed sign (which may depend on the order of the derivative). We present a short proof of Bernstein's theorem on the analyticity of such functions.",

keywords = "Analyticity, C-infinity functions, Regularly monotonie functions",

author = "McHugh, {J. A.M.}",

year = "1975",

month = feb,

doi = "10.1090/S0002-9939-1975-0354974-3",

language = "English (US)",

volume = "47",

pages = "358--360",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - A proof of bernsteins theorem on regularly monotonicf unctions

AU - McHugh, J. A.M.

PY - 1975/2

Y1 - 1975/2

N2 - A function is called "regularly monotonie" if it is of class C∞ and each derivative is of a fixed sign (which may depend on the order of the derivative). We present a short proof of Bernstein's theorem on the analyticity of such functions.

AB - A function is called "regularly monotonie" if it is of class C∞ and each derivative is of a fixed sign (which may depend on the order of the derivative). We present a short proof of Bernstein's theorem on the analyticity of such functions.

KW - Analyticity

KW - C-infinity functions

KW - Regularly monotonie functions

UR - http://www.scopus.com/inward/record.url?scp=84968512208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968512208&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1975-0354974-3

DO - 10.1090/S0002-9939-1975-0354974-3

M3 - Article

AN - SCOPUS:84968512208

SN - 0002-9939

VL - 47

SP - 358

EP - 360

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -

A proof of bernsteins theorem on regularly monotonicf unctions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this