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页数:30页
时间:2019-06-25
《广义函数空间上Drygas型函数方程的稳定性》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、᪥ṹ:10184ᑖ:O177.92ᳮắᦻᦪDrygasᦪḄឋTHESTABILITYOFDRYGASFUNCTIONALEQUATIONINTHESPACEOFDISTRIBUTION!"#Ạᦪ%&ᜧ万方数据理学硕士学位论文广义函数空间上Drygas型函数方程的稳定性王丹峰万方数据ᑖO177.92()UDC517_________________________200701458%&ᜧắᦻᦪDrygasᦪḄឋẆ+,-.!"/0ᓫ——~ᳮ
2、▾—ᢣ3ᦟ5-.、78>@Aᦟᣴ9:;#ẠᦪẆ+ᔣCᑖ᪆ᦻEFGH2010I05ᨴ20G万方数据KᦻLMᑮᳮắᦻ⌕PQRSᕒUVWQRSᕒUSᕒQRSᕒUSᕒQRSᕒUSᕒQRSᕒUSᕒ%&ᜧ2010I06ᨴ10G万方数据ᦻXYឋZ[K]^Z[:ᡠᕈFḄᦻaKᙠ35ᢣ3cXdeᡂḄẆ+ᡂg。iᡃᡠk,◀nᦻoᱯqrs᪗uvwxḄyᑖ,ᦻo{ᒹ}ᐸL⊤ᡈᑏḄẆ+ᡂg,{ᒹ}Kᦟ᪀ḄᡈᔊᵨḄᩞᧇ。ᡃḄKẆ+ᡠḄᙳLᙠᦻon[¡Ḅ¢[£⊤¤x¥。K§¨©Z[,ª¥
3、«¬ᵫ®¯Ḅᑗ±v²g。Ẇ+,³.:________________GH:IᨴGᦻᵨᣴᩗZ[Kᙠ35ᢣ3cᡠeᡂḄᦻ,᪥ᨵᩗ¶·ᐸᵯ¹vºᑴᦻ,½s¾▅ᡈÀÁÂKᦻḄᐰyᡈyᑖᑁÅ,½sᔣᨵᐵyÇᡈ᪀〈F£ᣴᩗᐸ¶·、¾▅ᡈÀÁÂKᦻḄᐰyᡈyᑖᑁÅ。ɶ(ᦻ,ᢥ¶(ḄᨵᐵËvÌᜐᳮ。KᦻÎÉ:1.¶(Ï,ᙠIÐ(²〉ᵨÉKZ[;2.{¶(Ï。Ẇ+,³.35³.GH:IᨴG万方数据要KᦻV⌕ÓnᙠÔÕᦪS'DrygasḄឋÖ⚪.®ᡃÙ✌ᐜᑭᵨpullbac
4、kÝÞḄḄC{ßàáᓄᦪ¥cḄãäḄDrygasᦪ{ßà。ᯠ²ᡃÙᑭᵨᐝçᓄè¹Ý{ßà,áᓄRn+1Ḅᐝçᦪ{ßà,PéᐝçᦪḄឋs²,êᑭᵨëᑣᓄᦪᦪíḄᐵa,PᦪDrygasᦪḄឋ。ᐵîï:Gaussðᣚ,òḄ᪶,Drygasᦪ,ឋ,ᦪ万方数据AbstractInthispaperweconsiderthestabilitytheoremsoftheDrygasequationinthespacesSofSchwartztemp
5、ereddistributions.MakinguseofpullbackwereformulateinequalitiesoffunctionsinthespaceS'(Rn)ofSchwartztempereddistributions.UsingmollifiertoconvertinequalitytosmoothfunctioninequalityinspaceofRn+1,wesolvethestabilityofsmoothfunction,thenbytherelationbetweenregularizi
6、ngfunctionandgeneralizedistribution,wehavethestabilityofDrygasfunction.Keywords:Gausstransforms,heatkernel,distributions,functionalequation,stabilityii万方数据ôõiAbstractii1416192021iii万方数据1*■■■■■■■»lillmm■V3ET/f"/ö÷øù>ᓃᦪឋẆ+üýIþÿḄẆ+⚞,LnᜧḄẆ+ᡂg3].ýᓝIḄ,ᐸẆ+ᑁ
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