Results 21 to 30 of about 5,762,325 (182)
Derivatives of Blaschke products [PDF]
Pacific Journal of Mathematics, 1984 This paper is a study of the behavior of the derivative of an infinite Blaschke product, focusing on membership of the derivative B' or fractional derivatives \(B^{\beta}\) in the classes \(A^{p,\alpha}\).
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Extreme values of the derivative of Blaschke products and hypergeometric polynomials [PDF]
Bulletin des Sciences Mathématiques, 2020 A finite Blaschke product, restricted to the unit circle, is a smooth covering map. The maximum and minimum values of the derivative of this map reflect the geometry of the Blaschke product.
L. Kovalev, Xuerui Yang
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Advances in Mathematics, 2013 We consider the classical problem of maximizing the derivative at a fixed point over the set of all bounded analytic functions in the unit disk with prescribed critical points. We show that the extremal function is essentially unique and always an indestructible Blaschke product. This result extends the Nehari--Schwarz Lemma and leads to a new class of
Kraus, Daniela, Roth, Oliver
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Blaschke inductive limits of uniform algebras
International Journal of Mathematics and Mathematical Sciences, 2001 We consider and study Blaschke inductive limit algebrasA(b), defined as inductive limits of disc algebras A(D) linked by a sequence b={Bk}k=1∞ of finite Blaschke products.
S. A. Grigoryan, T. V. Tonev
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Inner Functions in Lipschitz, Besov, and Sobolev Spaces
Abstract and Applied Analysis, 2011 We study the membership of inner functions in Besov, Lipschitz, and Hardy-Sobolev spaces, finding conditions that enable an inner function to be in one of these spaces.
Daniel Girela +2 more
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Maximal subalgebra of Douglas algebra
International Journal of Mathematics and Mathematical Sciences, 1988 When q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of H∞[q¯] to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B)⋂
Carroll J. Gullory
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A Burns-Krantz type theorem for Blaschke products [PDF]
Let $f$ be a holomorphic function mapping the open unit disk into itself. We establish a boundary version of Schwarz' lemma in the spirit of a result by Burns and Krantz and provide sufficient conditions on the local behaviour of $f$ near some boundary ...
Annika Moucha
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International Journal of Mathematics and Mathematical Sciences, 2001 We characterize the interpolating Blaschke products of finite type in terms of their support sets. We also give a sufficient condition on the restricted Douglas algebra of a support set that is invariant under the Bourgain map, and its minimal envelope ...
Carroll Guillory
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Inner functions in QK type spaces
Journal of Function Spaces and Applications, 2011 Inner functions in QK(p,q) are studied, provided K satisfies certain regularity conditions. In particular, it is shown that the only inner functions in QK(p, p-2), p≥1, are precisely the Blaschke products whose zeros {zn} satisfy supa∈D∑K(1-|φa(zn)|2)
Congli Yang
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On the differentiability of T(r,f)
International Journal of Mathematics and Mathematical Sciences, 1982 It is well known that T(r,f) is differentiable at least for r>r0. We show that, in fact, T(r,f) is differentiable for all but at most one value of r, and if T(r,f) fails to have a derivative for some value of r, then f is a constant times a quotient of ...
Douglas W. Townsed
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