简介:AradialfunctioncanbeexpressedbyitsgeneratorthroughThepositivedefiniteofthefunctionplaysanimportantroteintheradialbasisinterpolation.WecannaturallyuseBochner’sTheoremtocheckifispositivedefinite.Thisrequireshoweveran-dhnensiotialFouriertransformationanditisnotveryeasytocalculate.Furthermoreinalotofcaseswewilluseforspacesofvariousdimensionstoo,thenforeveryfixednweneeddotheFouriertransformationoncetocheckifthefunctionispositivedefiniteinthen-di-mensionalspace.Thecompletelymonotonefunction:,whichisdiscussedin[4]ispositivedefiniteforarbitraryspacedimensions.Withthistechniquetvecanveryeasilycharacterizethepositivedefinite,ofaradialfunctionthroughitsgenerator.Unfortunatelythereisonlyaverysmallsubsetofradialfunctionwhichiscompletelymonotone.Thusthiscriterionexcludedalotofinterestingfunctionssuchascompactlysupportedradialfunction,whcihareveryusefulinapplic
简介:AsequenceofsphericalzonaltranslationnetworksbasedontheBochner-RieszmeansofsphericalharmonicsandtheRieszmeansofJacobipolynomialsisintroduced,anditsdegreeofapproximationisachieved.Theresultsobtainedinthepresentpaperactuallyimplythattheapproximationofzonaltranslationnetworksisconvergentiftheactionfunctionshavecertainsmoothness.
简介:文章运用Orlicz空间和Lebesgue-Bochner空间理论及技巧,给出了Orlicz-Bochner空间在赋以Luxemburg范数时,球面上的点为各向一致凸点的充分性条件和空间具有各向一致凸性质的充要条件。
简介:Inthispaper,weconsiderthealmosteverywhereconvergencofBochner-RieszmeansbelowthecriticalindexinBesselpotentialspacesanda>0)andfindouttherelationbetweentheindexofBochner-Rieszmeansandthedegreeofsmoothnessoffunctions.
简介:本文中,我们研究一类由极大Bochner—Riesz算子和Lipschtz函数A生成的多线性算子,获得了它的(Lp,上q)型,而且我们还将证明此算子从Lebesgue空间到Lipschtz空间、从Herz空间到Campanato空间和从Lp空间到Tribel—Lizorkin空间的有界性.
简介:本文中,我们将一些作者的相关结论推广到加权空间,并且获得了由Bochner-Riesz算子生成的极大交换子在加权Herz-Hardy空间和加权Hardy空间的有界性,其中ω∈A_1.
简介:InthispaperwestudytheapproximationonsetoffullmeasureforfunctionsinSobolevspacesL_m~1(R~n)(m∈N)byBochner-RieszmeansofconjugaleFourierintegralsbelowthecriticalindex.AtheoremconcerningthepreciseapproximationorderswithrelationtothenumbermofspaceL_m~1(R~n)andtheindexofBochner-Rieszmeansisobtained.
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