SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON＇S EQUATION

In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is...

Full description

Saved in:
Bibliographic Details
Published in:数学物理学报：B辑英文版 2016 (3), p.791-801
Main Author: Bouikhalene BELAID Elqorachi ELHOUCIEN
Format: Article
Language:English
Subjects:
DTT
FCG
Wilson方程
一般形式
函数方程
局部紧群
泛函方程
稳定性定理
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 801
container_issue 3
container_start_page 791
container_title 数学物理学报：B辑英文版
container_volume
creator Bouikhalene BELAID Elqorachi ELHOUCIEN
description In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
format article
fullrecord <record><control><sourceid>chongqing</sourceid><recordid>TN_cdi_chongqing_primary_669027347</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cqvip_id>669027347</cqvip_id><sourcerecordid>669027347</sourcerecordid><originalsourceid>FETCH-chongqing_primary_6690273473</originalsourceid><addsrcrecordid>eNpjYuA0NDU30rU0sDBnYeA0MDIFss0MjDgYuIqLswwMDM2MzEw4GZyC_X1CQzz9_YIVHP1cFIJDHJ08fTxDIhX83RQcFdxd_VyDHH08oxxBSkBi4Z4-wf5-7_e0Byu4BoaChXkYWNMSc4pTeaE0N4OSm2uIs4duckZ-XnphZl56fEFRZm5iUWW8mZmlgZG5sYm5MVGKAKF-NUk</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON＇S EQUATION</title><source>ScienceDirect Freedom Collection 2022-2024</source><source>Springer Link</source><creator>Bouikhalene BELAID Elqorachi ELHOUCIEN</creator><creatorcontrib>Bouikhalene BELAID Elqorachi ELHOUCIEN</creatorcontrib><description>In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.</description><identifier>ISSN: 0252-9602</identifier><identifier>EISSN: 1572-9087</identifier><language>eng</language><subject>DTT ; FCG ; Wilson方程 ; 一般形式 ; 函数方程 ; 局部紧群 ; 泛函方程 ; 稳定性定理</subject><ispartof>数学物理学报：B辑英文版, 2016 (3), p.791-801</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/86464X/86464X.jpg</thumbnail><link.rule.ids>314,780,784,4024</link.rule.ids></links><search><creatorcontrib>Bouikhalene BELAID Elqorachi ELHOUCIEN</creatorcontrib><title>SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON＇S EQUATION</title><title>数学物理学报：B辑英文版</title><addtitle>Acta Mathematica Scientia</addtitle><description>In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.</description><subject>DTT</subject><subject>FCG</subject><subject>Wilson方程</subject><subject>一般形式</subject><subject>函数方程</subject><subject>局部紧群</subject><subject>泛函方程</subject><subject>稳定性定理</subject><issn>0252-9602</issn><issn>1572-9087</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNpjYuA0NDU30rU0sDBnYeA0MDIFss0MjDgYuIqLswwMDM2MzEw4GZyC_X1CQzz9_YIVHP1cFIJDHJ08fTxDIhX83RQcFdxd_VyDHH08oxxBSkBi4Z4-wf5-7_e0Byu4BoaChXkYWNMSc4pTeaE0N4OSm2uIs4duckZ-XnphZl56fEFRZm5iUWW8mZmlgZG5sYm5MVGKAKF-NUk</recordid><startdate>2016</startdate><enddate>2016</enddate><creator>Bouikhalene BELAID Elqorachi ELHOUCIEN</creator><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope></search><sort><creationdate>2016</creationdate><title>SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON＇S EQUATION</title><author>Bouikhalene BELAID Elqorachi ELHOUCIEN</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-chongqing_primary_6690273473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>DTT</topic><topic>FCG</topic><topic>Wilson方程</topic><topic>一般形式</topic><topic>函数方程</topic><topic>局部紧群</topic><topic>泛函方程</topic><topic>稳定性定理</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bouikhalene BELAID Elqorachi ELHOUCIEN</creatorcontrib><collection>维普_期刊</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>维普中文期刊数据库</collection><collection>中文科技期刊数据库- 镜像站点</collection><jtitle>数学物理学报：B辑英文版</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bouikhalene BELAID Elqorachi ELHOUCIEN</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON＇S EQUATION</atitle><jtitle>数学物理学报：B辑英文版</jtitle><addtitle>Acta Mathematica Scientia</addtitle><date>2016</date><risdate>2016</risdate><issue>3</issue><spage>791</spage><epage>801</epage><pages>791-801</pages><issn>0252-9602</issn><eissn>1572-9087</eissn><abstract>In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.</abstract></addata></record>
fulltext fulltext
identifier ISSN: 0252-9602
ispartof 数学物理学报：B辑英文版, 2016 (3), p.791-801
issn 0252-9602
1572-9087
language eng
recordid cdi_chongqing_primary_669027347
source ScienceDirect Freedom Collection 2022-2024; Springer Link
subjects DTT
FCG
Wilson方程
一般形式
函数方程
局部紧群
泛函方程
稳定性定理
title SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON＇S EQUATION
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T07%3A28%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-chongqing&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=SOLUTIONS%20AND%20STABILITY%20OF%20A%20GENERALIZATION%20OF%20WILSON%EF%BC%87S%20EQUATION&rft.jtitle=%E6%95%B0%E5%AD%A6%E7%89%A9%E7%90%86%E5%AD%A6%E6%8A%A5%EF%BC%9AB%E8%BE%91%E8%8B%B1%E6%96%87%E7%89%88&rft.au=Bouikhalene%20BELAID%20Elqorachi%20ELHOUCIEN&rft.date=2016&rft.issue=3&rft.spage=791&rft.epage=801&rft.pages=791-801&rft.issn=0252-9602&rft.eissn=1572-9087&rft_id=info:doi/&rft_dat=%3Cchongqing%3E669027347%3C/chongqing%3E%3Cgrp_id%3Ecdi_FETCH-chongqing_primary_6690273473%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_cqvip_id=669027347&rfr_iscdi=true