Abelian and Tauberian theorems relating the smoothness of an integrable function to the tail behavior of its Fourier transform /

Bibliographic Details
Main Author:	Cline, Daren B. H. (Author)
Corporate Author:	National Science Foundation (U.S.) (sponsoring body.)
Format:	Book
Language:	English
Published:	College Station, Texas : Department of Statistics, Texas A & M University, [1988]
Series:	Technical report (Texas A & M University. Department of Statistics) ; no. 88-8.
Subjects:	Distribution (Probability theory) Tauberian theorems. Fourier transformations. Functions of real variables. Smoothing (Statistics) Nonparametric statistics. Spectral energy distribution. Mathematical statistics. Probability theory and stochastic processes > Distribution theory > Distributions: general theory. Statistics > Nonparametric inference > Asymptotic properties. Statistics > Inference from stochastic processes > Spectral analysis. Regular variation

Description
Abstract:	We describe the precise relationship between the local smoothness behavior of an integrable function and the asymptotic tail behavior of its Fourier transform. This has special relevance for probability and spectral density functions with a discontinuous m-th derivative. Simply stated, if the function's Fourier transform is asymptotically as the product of an almost periodic function and a regularly varying function, then an m-th derivative of the function behaves at its discontinuities like the density of a regularly varying function. With side conditions, the converse also holds.
Item Description:	Offprint: Journal of mathematical analysis and applications. "5/27/88"--Leaf [i]. Funding information taken from leaf [i].
Physical Description:	24 leaves ; 28 cm
Bibliography:	Includes bibliographical references (leaf 24).