免费论文摘要：Sierpinski垫上的正交系

正文接洽了自仿猜想的非谱题目.重要目的是在一类自仿猜想下,估量Sierpinski垫上正交系的基数.正文的重要截止如次:1.接洽到蔓延整矩阵和数字集:$$ M= left[                                egin{array}{cc}                                 a & b                                  c & d                                  end{array}                  ight], D=left{                                           egin{array}{c}                                             left(                                 egin{array}{c}                                   0                                    0                                    end{array}                               ight),                              left(                                 egin{array}{c}                                   1                                    0                                    end{array}                               ight),left(                                 egin{array}{c}                                   0                                    1                                  end{array}                               ight)                                 end{array}                                ight}$$的自仿猜想$mu_{M,D}$的维持在迭代因变量系${phi_{d} (x)=M^{-1}(x+d)}_{din D}$的吸媒介上,个中$(a+d)^2=4(ad-bc)$而且3不整除a+d. 开始获得了自仿猜想的傅里叶变幻$hat{mu}_{M,D}$的零集$Z(hat{mu}_{M,D})$的少许表白本质,其次用大略的本领获得了几个有效的截止.结果运用自仿猜想傅里叶变幻$hat{mu}_{M,D}$的零集$Z(hat{mu}_{M,D})$的那些本质证领会$L^2(mu_{M,D})$空间中有且惟有3个彼此正交的指数因变量.2.接洽到蔓延整矩阵和数字集:$$M=left[egin{array}{ccc}p & 0 & m & p & 0 & 0 & p end{array}ight], D=left{                egin{array}{c}                  left(egin{array}{c}0 end{array}ight),left(egin{array}{c}1 end{array}ight),left(egin{array}{c}0 1 end{array}ight),left(egin{array}{c}0 1  end{array} ight)  end{array} ight}$$                               的自仿猜想$mu_{M,D}$的维持在广义三维Sierpinski垫T(M,D)上,个中p是单数.在第三章先证领会在$L^2(mu_{M,D})$空间中最多生存7个彼此正交的指数因变量,并运用这个本领估量了当数字集有四个元素时平面Sierpinski垫上正交指数因变量的个数.结果当m=0时,证领会在三维Sierpinski垫上最多生存4个彼此正交的指数因变量.上述接洽截止辨别实行了Dutkay, Jorgensen, Li以及Pedersen等人的相映论断,对进一步深沉领会自仿猜想的谱本质有要害效率.

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