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21.
Curtis T. McMullen 《Geometric And Functional Analysis》2009,18(6):2101-2119
We show the space of expanding Blaschke products on S1 is compactified by a sphere of invariant measures, reminiscent of the sphere of geodesic currents for a hyperbolic surface.
More generally, we develop a dynamical compactification for the Teichmüller space of all measure preserving topological covering
maps of S1.
Research supported in part by the NSF. 相似文献
22.
23.
《复变函数与椭圆型方程》2012,57(3):255-258
It is shown that a finite Blaschke product with finite poles, has a nonzero residue. The proofs for the two types of Blaschke products are essentially different. 相似文献
24.
Yan Wu & Xianmin Xu 《数学研究通讯:英文版》2009,25(1):19-29
In this paper, we prove that the Toeplitz operator with finite Blaschke
product symbol $S_{ψ(z)}$ on $N_ϕ$ has at least $m$ non-trivial minimal reducing subspaces,
where $m$ is the dimension of $H^2(Γ_ω) ⊖ ϕ(ω)H^2
(Γ_ω)$. Moreover, the restriction
of $S_{ψ(z)}$ on any of these minimal reducing subspaces is unitary equivalent to the
Bergman shift $M_z$. 相似文献
25.
E. I. Yashagin 《Siberian Mathematical Journal》2007,48(4):762-766
We construct an example of a maximal unimodular Dirichlet algebra whose one-point Gleason parts are dense in the maximal ideal space. The main statements were announced in [1] and now we provide their complete proofs. 相似文献
26.
John R. Akeroyd 《Journal of Mathematical Analysis and Applications》2022,505(2):125525
We modify an idea in an earlier paper to enlarge the collection of inner functions that are known to be in the uniform closure of the indestructible Blaschke products. 相似文献
27.
Let M2 be an umbilic-free surface in the unit sphere S3. Four basic invariants of M2 under the Moebius transformation group of S3 are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form Φ. We call the Blaschke tensor is isotropic if there exists a smooth function λ such that A = λg. In this paper, We classify all surfaces with isotropic Blaschke tensor in S3. 相似文献
28.
Given an immersed submanifold x : M^M → S^n in the unit sphere S^n without umbilics, a Blaschke eigenvalue of x is by definition an eigenvalue of the Blaschke tensor of x. x is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. Then the classification of Blaschke isoparametric hypersurfaces is natural and interesting in the MSbius geometry of submanifolds. When n = 4, the corresponding classification theorem was given by the authors. In this paper, we are able to complete the corresponding classification for n = 5. In particular, we shall prove that all the Blaschke isoparametric hypersurfaces in S^5 with more than two distinct Blaschke eigenvalues are necessarily Mobius isoparametric. 相似文献
29.
A. D. Baranov 《Proceedings of the American Mathematical Society》2006,134(10):3003-3013
We study boundedness of the differentiation and embedding operators in the shift-coinvariant subspaces generated by Blaschke products with sparse zeros, that is, in the spaces of meromorphic functions with fixed poles in the lower half-plane endowed with -norm. We answer negatively the question of K.M. Dyakonov about the necessity of the condition for the boundedness of the differentiation on . Our main tool is a construction of an unconditional basis of rational fractions in .
30.
Daniel Girela Cristó bal Gonzá lez José Á ngel Pelá ez 《Proceedings of the American Mathematical Society》2006,134(5):1309-1314
A subspace of the Hardy space is said to have the -property if whenever and is an inner function with . We let denote the space of Bloch functions and the little Bloch space. Anderson proved in 1979 that the space does not have the -property. However, the question of whether or not ( ) has the -property was open. We prove that for every the space does not have the -property.
We also prove that if is any infinite Blaschke product with positive zeros and is a Bloch function with , as , then the product is not a Bloch function.