A claim on convolution and kernel

Article View: bit.listserv.stat-l

Article #3650

Back to bit.listserv.stat-l Previous Next

#3650

From: Shinichi Sakata
Date: Sat, 09 Nov 1991 00:31

28 lines
1256 bytes

Hi everyone. I am interested in the following claim.

CLAIM:
                    d
Let f and K be L (R ) functions and assume that
                1

    /
   | 
   |    K(y)  dy  = 1.
   |  d
  /  R

Then


    /
   |               1
   |      f(x-y) ----- K(y/h) dy  ---> 0     as h ---> +oo.
   |                d
   |  d            h
  /  R


  Does anyone know wheter the above claim is correct or not when we
do not assume boundedness of f or K?

   Shinichi

Technical Details

Message-ID: <1991Nov9.003102.12837@network.ucsd.edu>

Path:

arc1-ca.pugleaf.net!gmdzi!unido!fauern!ira.uka.de!yale.edu!spool.mu.edu!uwm.edu!wupost!sdd.hp.com!ucsd!network.ucsd.edu!weber.ucsd.edu!ssakata

Show Full Headers

Complete Article Headers

X-Google-Language: ENGLISH,ASCII-7-bit
X-Google-Thread: 10c242,7b5c9720d656b9c9,start
X-Google-Attributes: gid10c242,public
X-Google-Thread: f5efb,7b5c9720d656b9c9,start
X-Google-Attributes: gidf5efb,public
X-Google-ArrivalTime: 1991-11-09 06:11:24 PST
Path: arc1-ca.pugleaf.net!gmdzi!unido!fauern!ira.uka.de!yale.edu!spool.mu.edu!uwm.edu!wupost!sdd.hp.com!ucsd!network.ucsd.edu!weber.ucsd.edu!ssakata
From: ssakata@weber.ucsd.edu (Shinichi Sakata)
Newsgroups: bit.listserv.stat-l,sci.math.statistics
Subject: A claim on convolution and kernel
Message-ID: <1991Nov9.003102.12837@network.ucsd.edu>
Date: 9 Nov 91 00:31:02 GMT
Sender: usenet@network.ucsd.edu (News System)
Organization: University of California, San Diego
Lines: 28
Nntp-Posting-Host: weber.ucsd.edu