Construction of orthonormal basis on self-similar sets by generalized permutative representations of the Cuntz algebras
نویسندگان
چکیده
A systematic construction method of orthonormal basis on self-similar sets is given by the use of representations of the Cuntz algebras. We introduce two kinds of orthonormal basis of self-similar sets including explicit description for the Cantor set, the Sierpiński gasket and the Sierpiński carpet.
منابع مشابه
Generalized permutative representations of the Cuntz algebras . III — Generalization of chain type —
In our previous papers([10, 11]), we introduce a class of representations of the Cuntz algebra ON which is a generalization of permutative representations with cycle by [5, 7, 8]. As application, we have results about quantum field theory([1, 2, 3, 4]), fractal sets([14]) and dynamical systems([13, 15, 16, 17]). We continue to treat chain case in this paper. The remarkable results are that this...
متن کاملGeneralized Permutative Representations of the Cuntz Algebras. Iv —gauge Transformation of Representations—
Nowadays, gauge theory is well established as the fundamental theories of physics([18]). The origin of gauge theory was introduced by H.Weyl in the 1920’s and it is treated as fiber bundle and geometry of connection by C.N.Yang and K.L.Mills([17]). We introduce another aspect of gauge theory in a subject of representation theory of operator algebra. Since the original purpose of gauge theory in...
متن کاملRepresentations of the Cuntz - Krieger algebras . II — Permutative representations —
We generalize permutative representations of the Cuntz algebras for the Cuntz-Krieger algebra OA for any A. We characterize cyclic permutative representations by notions of cycle and chain, and show their existence and uniqueness. We show necessary and sufficient conditions for their irreducibility and equivalence. In consequence, we have a complete classification of permutative representations...
متن کاملGeneralized permutative representations of the Cuntz algebras
We introduce representations of the Cuntz algebra ON which are parameterized by sequences in the set of unit vectors inC . These representations are natural generalization of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of represen...
متن کاملGeneralized permutative representations of Cuntz algebras
We introduce representations of the Cuntz algebra ON which are parameterized by sequences in the set of unit vectors inC . These representations are natural generalizations of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of represe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003