The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal ...The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal dimension of L(x).展开更多
We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding i...We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolani to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Pade interpolation to a finite set of functions.展开更多
We introduce the tracial limit A = （t4）lim n→∞（An,pn） and show that if K0（An） has ordered relation, K0（A） has ordered relation naturally. In the case that A is simple and K0（An） is weakly unperforated for ...We introduce the tracial limit A = （t4）lim n→∞（An,pn） and show that if K0（An） has ordered relation, K0（A） has ordered relation naturally. In the case that A is simple and K0（An） is weakly unperforated for every n, K0（A） is weakly unperforated too. Furthermore, the Riesz interpolation property of K0（An） can be transmitted to K0（A）.展开更多
The note studies certain distance between unitary orbits.A result about Riesz interpolation property is proved in the first place.Weyl(1912) shows that dist(U(x),U(y))= δ(x,y) for self-adjoint elements in matrixes.Th...The note studies certain distance between unitary orbits.A result about Riesz interpolation property is proved in the first place.Weyl(1912) shows that dist(U(x),U(y))= δ(x,y) for self-adjoint elements in matrixes.The author generalizes the result to C*-algebras of tracial rank one.It is proved that dist(U(x),U(y)) = D_(c)(x,y) in unital AT-algebras and in unital simple C*-algebras of tracial rank one,where x,y are self-adjoint elements and D_(C)(x,y) is a notion generalized from δ(x,y).展开更多
文摘The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal dimension of L(x).
文摘We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolani to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Pade interpolation to a finite set of functions.
基金The NNSF (10271090) of China and Shanghai Priority Academic Discipline.
文摘We introduce the tracial limit A = （t4）lim n→∞（An,pn） and show that if K0（An） has ordered relation, K0（A） has ordered relation naturally. In the case that A is simple and K0（An） is weakly unperforated for every n, K0（A） is weakly unperforated too. Furthermore, the Riesz interpolation property of K0（An） can be transmitted to K0（A）.
文摘The note studies certain distance between unitary orbits.A result about Riesz interpolation property is proved in the first place.Weyl(1912) shows that dist(U(x),U(y))= δ(x,y) for self-adjoint elements in matrixes.The author generalizes the result to C*-algebras of tracial rank one.It is proved that dist(U(x),U(y)) = D_(c)(x,y) in unital AT-algebras and in unital simple C*-algebras of tracial rank one,where x,y are self-adjoint elements and D_(C)(x,y) is a notion generalized from δ(x,y).
