Hankel Transforms of General Monotone Functions

Alberto Debernardi

doi:10.1007/978-3-030-12277-5_5

Hankel Transforms of General Monotone Functions

Alberto Debernardi

Department of Mathematics

Mathematics Research Center

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

5 Scopus citations

Abstract

We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel–Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.

Original language	English
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	87-104
Number of pages	18
DOIs	https://doi.org/10.1007/978-3-030-12277-5_5
State	Published - 2019

Publication series

Name	Applied and Numerical Harmonic Analysis
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Boundedness
Cosine series
General monotonicity
Hankel transform
Uniform convergence

Access to Document

10.1007/978-3-030-12277-5_5

Cite this

@inbook{3aae64e2d81d4cc3a3d39e5288fb51fb,

title = "Hankel Transforms of General Monotone Functions",

abstract = "We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel–Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.",

keywords = "Boundedness, Cosine series, General monotonicity, Hankel transform, Uniform convergence",

author = "Alberto Debernardi",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

doi = "10.1007/978-3-030-12277-5\_5",

language = "אנגלית",

series = "Applied and Numerical Harmonic Analysis",

publisher = "Springer International Publishing",

pages = "87--104",

booktitle = "Applied and Numerical Harmonic Analysis",

}

TY - CHAP

T1 - Hankel Transforms of General Monotone Functions

AU - Debernardi, Alberto

PY - 2019

Y1 - 2019

N2 - We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel–Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.

AB - We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel–Olivier test for real-valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series.

KW - Boundedness

KW - Cosine series

KW - General monotonicity

KW - Hankel transform

KW - Uniform convergence

UR - https://www.scopus.com/pages/publications/85074654986

U2 - 10.1007/978-3-030-12277-5_5

DO - 10.1007/978-3-030-12277-5_5

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:85074654986

T3 - Applied and Numerical Harmonic Analysis

SP - 87

EP - 104

BT - Applied and Numerical Harmonic Analysis

PB - Springer International Publishing

ER -

Hankel Transforms of General Monotone Functions

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this