在广义函数空间上Wilson函数方程的稳定性

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1、᪥ṹ：10184ᑖ：O177.92ᳮắᦻᙠᦪWilsonᦪḄឋStabilityofWilsonFunctionalEquationinspacesofgeneralizedfunctions!"#Ạᦪ%&ᜧ万方数据理学硕士学位论文在广义函数空间上wilson函数方程的稳定性崔丽英万方数据ᑖO177.92./UDC517___________________200701450_____________%&ᜧắᦻᙠᦪWilsonᦪḄឋẆ1234!"56ᓫ——■ᳮ▾—ᢣ9ᦟ;34

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6、ᙠᦪ，a⌕ᑭᵨḄ᪶，ᦪᑣWilsonᱯ-ᦪḄHyers-Ulamឋ。ᐵ：Wilsonᦪ，ᦪ，Ḅ᪶，Hyers-Ulamឋ万方数据AbstractHyers-UlamstabilityofWilsonfunctionalequation,thatis,thegeneralizedd’Alembertfunctionalequationaremainlystudiedinthepaper.Firstly,byusedtheunboundednessoffunctions,thestabilityofWil

7、sonfunctionalequationisobtainedinthespaceofcontinuousfunctions.Andthenusingheatkernelandtheapproachofregularizinggeneralizedfunctions,stabilityofWilsonfunctionalequationisgiveninthespacesofgeneralizedfunctionssuchastheSchwartztempereddistributions,FourierhyperfunctionsandGelfand-shil

8、ovgeneralizedfunctions.Keywords:Wilsonfunctionalequation;distributions;heatkernel;Hyers-Ulamstabilityii万方数据iAbstractii__ztzzpI-zbr-i12ᙠstᦪWilsonᦪḄឋ5ᙠᦪWilsonᦪḄឋ12192021iii万方数据RaiS]ᦪឋẆ1S ḄẆ1⚞¢，W£¤lᜧ¥ḄẆ1ᡂ§¨3].©ªᓝSḄ¬，ᐸẆ1ᑁ°±²³W´ᑮᦪḄµ¶⚞¢，ᐸẆ1·¸±¹ºᕈ¶᪵ឋ。BakerJ½²¾¿ᦪḄ

9、Hyers-Ulampᦪឋ}ÀlẆ1，¤ᑮlµ¶Ẇ1ᡂ§ÁªSChungJ½ÂÃᦪḄឋẆ1mᑮᦪ，Ĥᑮl~ÅÆ⌕ǧ[6-8]。ᑮÉÊË，²WilsonᐵÌd’AlembertᦪḄm·¸，ᓽWilsonᦪ：/(x+y)+g(x~y)~h{x)k{y)=0(1.1)ḄHyers-UlampឋÍÎᨵÐẆ1’ᐸÑ/,Òh,k:Rn—RḄᦪ。ÊÓVᦻᑖWilsonHyers-UlamWilsonHyers-Ulamឋ；ᯠ

10、ᙠÓ#Ạ，Ô␺ᦻÖ[^8]L×Ḅ¹，ᑭᵨḄ᪶，²ᦪSchwartz-Wi

11、lsonHyers-Ul