简介：论述了Dirichlet函数在实变函数中的应用。通过Dirichlet函数进一步理解了实变函数中的简单函数、几乎处处成立的概念,明确了可测函数与连续函数、Riemann可积与Lebesgue可积的关系。

简介：通过对一类独立随机变量序列所决定的Dirichlet级数的研究，得出一个结果：右半平面上有限级的随机Dirichlet级数几乎必然没有亏函数．

简介：对于由广义Dirichlet级数表示，并且在固定带形有界、不恒为零的整函数的存在性，给出了充要条件。

简介：系统地研究了全平面收敛的B-值随机Difichlet级数的增长性，得到了在一定条件下，B-值随机Dirichlet级数在收敛平面上的增长（下）级几乎处处等于某Dirichlet级数的增长（下）级还得到了它们与指数和系数的关系式．

简介：引用了Knopp-Kojima的方法，在没有指数条件下讨论了全平面内收敛无限级Dirichlet级数的增长性，得到了2个结果。

简介：ThisarticleinvestigatestheconvergenceandgrowthofmultipleDirichletseries.TheValironformulaofDirichletseriesisextendedton-tupleDirichletseriesandanequivalencerelationbetweentheorderofn-tupleDirichletseriesanditscoefficientsandexponentsisobtained.

简介：TheautomorphismgroupoftheToeplitzC^*-algebra,J(C^1),generatedbyToeplitzop-eratorswithC^1-symbolsonDirichletspaceDisdiscussed;theK0,K1-groupsandthefirstcohomologygroupofJ(C^1)arecomputed.Inaddition,theauthorprovesthatthespectraofToeplitzoperatorswithC^1-symbolsarealwaysconnected,anddiscussesthealgebraicprop-ertiesofToeplitzoperators.Inparticular,itisprovedthatthereisnonontrivialselfadjointToeplitzoperatoronDandTψ^*=Tψ^-ifandonlyifTψisascalaroperator.

简介：在这篇文章，Dirichlet系列的唯一定理被证明。然后在权利的随机的Dirichlet系列半飞机被学习，并且有限顺序的随机的Dirichlet系列几乎肯定有的结果(a.s)没有缺乏的功能被证明。给词调音：随机的系列；Dirichlet系列；缺乏的多项式；价值分发

简介：Aclassofsingularlyperturbedboundaryvalueproblemwithsingularitiesisconsidered.Introducingthestretchedvariables,theboundarylayercorrectivetermsnearx=0andx=1areconstructed.Undersuitableconditions,byusingthetheoryofdifferentialinequalitiestheexistenceandasymptoticbehaviorofsolutionforboundaryvalueproblemareproved,uniformlyvalidasymptoticexpansionofsolutionwithboundarylayersareobtained.更多还原

简介：Inthispaper,theauthorstudiestheregularityofsolutionstotheDirichletproblemforequationLu=f,whereLisasecondorderdegenerateellipticoperatorindivergenceforminΩ,aboundedopensubsetofRn(n≥3).

简介：1.IntroductionactEbeaHa~tOPologicalspaceandmamdritemeasureonitsBorela-algebraB(E).In[11,MOSCointroducedthefollowingnow-calledMoscoconvergenceofsyllUnetricac~l~:tlf621i.t,..2.1].AsequenceofsynUnetricbilinearforms(En,D(en)),nEN,issaidtoMO8coconvergetoa...

简介：ThevaluedistributionofentirefunctionsdefinedbyDirichletseriesarestudiedinthispresentarticle.ItisprovedthatentirefunctionsdefinedbyDirichletserieshavethepitsproperty,whichimprovetherelativeresultsonlacunaryTaylorseriesobtainedbyLittlewoodJ.E.andOffordA.C.

简介：Inthispaper,ageneralalgorithmforthecomputationoftheFouriercoefficientsof2π-periodic(continuous)functionsisdevelopedbasedonDirichletcharacters,GausssumsandthegeneralizedM¨obiustransform.ItpermitsthedirectextractionoftheFouriercosineandsinecoefficients.Threespecialcasesofouralgorithmarepresented.AVLSIarchitectureispresentedandtheerrorestimatesaregiven.

简介：UsingvariationalmethodsandMorsetheory,weobtainsomeexistenceresultsofmultiplesolutionsforcertainsemilinearproblemsassociatedwithgeneralDirichletforms.

简介：Thispaperisdevotedtothestudyofsecondordernonlineardifferenceequations.ANonlocalPerturbationofaDirichletBoundaryValueProblemisconsidered.AnexhaustivestudyoftherelatedGreen'sfunctiontothelinearpartisdone.Theexactexpressionofthefunctionisgiven,moreovertherangeofparameterforwhichithasconstantsignisobtained.Usingthis,someexistenceresultsforthenonlinearproblemarededucedfrommonotoneiterativetechniques,theclassicalKrasnoselskifixedpointtheoremorbyapplicationofrecentfixedpointtheoremsthatcombineboththeories.

简介：这份报纸与Dirichlet-Neumann状况处理nonhomogeneous绳的周期的答案的存在。作者考虑时期是荒谬的盒子空格长度多重并且为某荒谬的数字证明那，零不是联系线性操作符的光谱的累积点。这结果能被用来证明周期的答案的存在避免使用Nash-Moser重复。

简介：几个Galerkin-Petrov方法，包括的多项式搭配和分析元素的集中在Dirichlet空间的Toeplitz操作员的搭配方法，被建立。特别地，如果基础和测试功能拥有某些圆形的对称，如此的方法收敛，这被显示出。给词调音：GalerkinPetrov方法；多项式搭配；分析元素搭配；Toeplitz操作员；Dirichlet空间

简介：InthispaperweprovideaprobabilisticapproachtothefollowingDirichletProblem{(∑x4(αijxj)+∑bixi+ξ)u=0,iDu=g,onD,withoutassumingthattheeigenvaluesoftheoperator∑xi(αijxj)+∑bixi+ξwithDirichletboundaryconditionsareallstrictlynegative.TheresultsofthispapergeneralizedthoseofMa.

简介：LetDbeaboundedC3-domaininRdand(aij)beaboundedsymmetricmatrixdefinedonD.Considerthesymmetricform（u,v）=1/2∫Daij（x）（u（x））/（xi）（v（x））/（xj）dx,u,v∈H1（D）.UndersomeassumptionsitisshownthatthediffusionprocessassociatedwiththeregularDirichletspace(,（H1（D））onL2（D）canbecharacterizedasauniquesolutionofacertainstochasticdifferentialequation.

简介：Letubeaweaksolutionof(-△)mu=fwithDirichletboundaryconditionsinasmoothboundeddomainΩRn.Then,themaingoalofthispaperistoprovethefollowingaprioriestimate:‖u‖Wω2m,p(Ω)≤C‖f‖Lωp(Ω),whereωisaweightintheMuckenhouptclassAp.