Results 21 to 30 of about 14,879 (215)
Clark measures and a theorem of Ritt [PDF]
, 2018 We determine when a finite Blaschke product B can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt's problem) in terms of the Clark measure for B. Our tools involve the numerical range of compressed shift operators
Chalendar, I +3 more
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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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Blaschke products and Nevanlinna-Pick interpolation [PDF]
, 2015 For a Nevanlinna{Pick problem with more than one solution, Rolf Nevanlinna proved that all extremal solutions are inner functions. If the interpolation points are contained in dinitely many cones terminating at the unit circle, it is shown that all ...
Stray, Arne
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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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Semicrossed products of the disk algebra and the Jacobson radical
, 2012 We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical of these operator algebras.
Anchalee Khemphet +10 more
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A uniqueness theorem for meromorphic functions
Математичні СтудіїIn this paper, we prove the uniqueness theorem for a special class of meromorphic functions on the complex plane $\mathbb{C}$. In particular, we study the class of meromorphic functions $f$ in the domain $\mathbb{C}\setminus K'$, where $K'$ is the finite
N. Sushchyk, D. Lukivska
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Composition and decomposition of indestructible Blaschke products
, 2013 We prove that the composition of two indestructible Blaschke products is again an indestructible Blaschke product. We also show that if an indestructible Blaschke product is the composition of two bounded analytic functions, then both functions are ...
Kraus, Daniela, Roth, Oliver
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The radial behavior of Blaschke products [PDF]
Proceedings of the American Mathematical Society, 1985 The paper extends results of G. T. Cargo and of C. L. Belna, F. W. Carroll and G. Piranian on the existence of Blaschke products with prescribed radial limits at a prescribed finite or countable set of points on the unit circle. The extension permits the prescription of the radial cluster set at each point of a prescribed countable set on the unit ...
Belna, C. L., Colwell, P., Piranian, G.
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Destructible and Indestructible Blaschke Products [PDF]
Transactions of the American Mathematical Society, 1980 A special case of destructibility for Blaschke products is introduced and studied. An example is given of a destructible Blaschke product which becomes indestructible when a single point is deleted from its zero-set.
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