The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on t...The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).展开更多
We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is ob...We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the Hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausforff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system. Our methods are applicable to some iterated function systems that do not satisfy the finite type condition recently introduced by Ngai and Wang.展开更多
基金This work supported by the National Natural Science Foundation of China(Grant No.10571084)
文摘The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).
文摘We provide a simple formula to compute the Hausdorff dimension of the attractor of an overlapping iterated function system of contractive similarities satisfying a certain collection of assumptions. This formula is obtained by associating a non-overlapping infinite iterated function system to an iterated function system satisfying our assumptions and using the results of Moran to compute the Hausdorff dimension of the attractor of this infinite iterated function system, thus showing that the Hausforff dimension of the attractor of this infinite iterated function system agrees with that of the attractor of the original iterated function system. Our methods are applicable to some iterated function systems that do not satisfy the finite type condition recently introduced by Ngai and Wang.
