向量細(xì)分格式的收斂階和高維Riesz小波基.pdf

1、浙江大學(xué)理學(xué)院博士學(xué)位論文向量細(xì)分格式的收斂階和高維Riesz小波基姓名：劉志松申請(qǐng)學(xué)位級(jí)別：博士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：李松20080401AbstractInthispaperweinvestigatethefollowingthreesubjects：1Theconvergencerateofhomogeneousandnonhomogeneousmultiplevectorrefinementequationsoftheform

2、and妒(z)=∑n(口)妒(訛一Q)，z∈科，Q∈Zs妒(z)=∑a(oOqa(Mx—Q)9(z)，z∈R8，Q∈Zswherethevectoroffunctions妒=(妒1，，協(xié))Tbelongsto(LI(R8))7，a：=(o(Q))口∈Z。isafinitelysupportedsequenceofrXrmatricescalledrefinementmaskandMisan8sintegermatrixsuchthatl

3、imM咖=0，g=(gl，，肼)risagivenfinitelysupportedfunctiononR82Startingfromapairofbiorthogonalrefinablefunctions仍驢，letm=IdetMI，define礦(z)=∑乩(口)妒(Mz—Q)，z∈IR∥=1，，m一1，口∈Zs移p(z)=∑配(口)9(Mz—Q)，z∈R8，∥=1，，m一1n∈Z。Then矽and妒generatetwoRies

4、zbasesforL2(R3)，ifforany∈∈R8，z，=1，，m一1，thefollowingconditionsaresatisfied：m一1∑a(M刁27rM習(xí)饑)6p(M習(xí)21rM坷饑)‘=o；m1∑配(M一丁27rM—T饑)a(M—T∈2丌M—r饑)=o；t=OdetB(∈)≠03Providingtwoexamplestoshowtheoremgiveninpart2KeyWords：refinementequati