  We study the extended Anderson model on the two-dimensional Penrose lattice,
combining the real-space dynamical mean-field theory with the non-crossing
approximation. It is found that the Coulomb repulsion between localized and
conduction electrons does not induce a valence transition, but the crossover
between the Kondo and mixed valence states in contrast to the conventional
periodic system. In the mixed-valence region close to the crossover, nontrivial
valence distributions appear characteristic of the Penrose lattice,
demonstrating that the mixed-valence state coexists with local Kondo states in
certain sites. The electric reconstruction in the mixed valence region is also
addressed.
