广义Sierpinski垫上正交指数函数的个数

The Cardinality of Orthogonal Exponential Functions on the Generalized Sierpinski Gasket

联系到扩张整矩阵和数字集M=[p1p4p60p2p50 0p3 ]D={[000],[100],[010],[001]的自仿测度μM,D是非谱测度.其中pi∈2Z+1(i=1,2,3);pi∈Z且|pi|>1(i=4,5,6);p2|p4且p3|pi(i=5,6).证明了在L2(μM,D)空间上最多存在4个相互正交的指数函数且4是最好估计.

The self-affine measure μM,D corresponding to the expanding integer matrix and numeral setM=[p1p4p60p2p500p3]D={[000],[100],[010],[001]is a non-spectral measure,where pi∈2Z＋1（i=1,2,3）;pi∈Z,｜pi｜1（i=4,5,6）;p2｜p4 and p3｜pi（i=5,6）.We show that there exist at most 4 mutually orthogonal exponential functions in L2（μM,D） and the number 4 is the best.