Dirichlet Form of Product of Variational Fractals

completed.□　Lemma2 .2　 Suppose H to be a Hilbert spacewith the inner product ( .,.) H and the relativenorm‖·‖H.If{xn}in H weakly converges tox,then there exists a subsequence {xni}satisfyingthatx - 1k ki=1xni H→ 0 ,　 k→∞ .　The proof can be found in Ref.[9].　 Lemma 2 .3　 Suppose W* to be a symmetricform on D[W],and W* [u]≤ W1[u]for all u∈D[W].If {un}∈D[W]in H converges W1- weak-ly to u,then it converges W* - weakly to u.　The proof can be found in Ref.[8].　 Lemma 2 .4…

Dirichlet Form of Product of Variational Fractals

Much effort has gone into constructing Dirichlet forms to define Laplacians on self-similar sets. However, the results have only been successful on p.c.f. (post critical finite) fractals. We prove the existence of a Dirichlet form on a class of non- p.c.f. sets that are the product of variational fractals.