On Abel-Tauber theorems for Fourier cosine transforms
type: Item
instance of: scholarly article
title: On Abel-Tauber theorems for Fourier cosine transforms
zbMATH Open document ID: 0849.42007
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-03-31T00:00:00Z
review text: The aim of the paper is to prove Abel-Tauber theorems for Fourier cosine series and integrals which are closely related to results of Pitman and Soni and Soni. The asymptotic behaviour \(f(t)\sim t^{- 1}\) for \(t\to \infty\) is characterized in terms of the Fourier cosine transform of \(f\), where \(f\) is a locally integrable eventually non-increasing function on \([0, \infty)\) with \(\lim_{t\to \infty} f(t)= 0\). Applications to probability distributions and stationary processes are given.
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 861848
zbMATH Keywords: slowly varying functions
zbMATH Keywords: Abel-Tauber theorems
zbMATH Keywords: Fourier cosine transform
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1440
OpenAlex ID: W2005894511
DOI: 10.1006/JMAA.1995.1440
description: scientific article; zbMATH DE number 861848