Constructive Approximation, ISSN 0176-4276, 8/2011, Volume 34, Issue 1, pp. 1 - 21

This research is partially a continuation of a 2007 paper by the author. Growth estimates for generalized logarithmic derivatives of Blaschke products...

Exponential sequence | 34C10 | 30D50 | Oscillation theory | Blaschke-oscillatory equation | Mathematics | 34M10 | Frequency of zeros | 46B70 | Interpolating sequence | Analysis | Numerical Analysis | Blaschke product | Logarithmic derivative | Prescribed zero sequence | MATHEMATICS | STOLZ | DERIVATIVES

Exponential sequence | 34C10 | 30D50 | Oscillation theory | Blaschke-oscillatory equation | Mathematics | 34M10 | Frequency of zeros | 46B70 | Interpolating sequence | Analysis | Numerical Analysis | Blaschke product | Logarithmic derivative | Prescribed zero sequence | MATHEMATICS | STOLZ | DERIVATIVES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2012, Volume 364, Issue 5, pp. 2319 - 2337

We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product...

Circles | Integers | Algebra | Mathematical theorems | Analytic functions | Applied mathematics | Subalgebras | Subharmonics | Mathematical functions | Angular derivative | Blaschke product | Interpolating blaschke product | MATHEMATICS | interpolating Blaschke product | COMPOSITION OPERATORS | angular derivative | SEQUENCES

Circles | Integers | Algebra | Mathematical theorems | Analytic functions | Applied mathematics | Subalgebras | Subharmonics | Mathematical functions | Angular derivative | Blaschke product | Interpolating blaschke product | MATHEMATICS | interpolating Blaschke product | COMPOSITION OPERATORS | angular derivative | SEQUENCES

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 260, Issue 7, pp. 2086 - 2147

Let H ∞ be the Banach algebra of bounded analytic functions on the open unit disk D . Let G be the union set of all nontrivial Gleason parts in the maximal...

Algebra of bounded analytic functions | Carleson–Newman Blaschke product | Interpolating Blaschke product | Big disk algebra | Gleason part | Ideal theory | Carleson-Newman Blaschke product

Algebra of bounded analytic functions | Carleson–Newman Blaschke product | Interpolating Blaschke product | Big disk algebra | Gleason part | Ideal theory | Carleson-Newman Blaschke product

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 259, Issue 4, pp. 975 - 1013

... ) at x in E, using the geometrical words of E. We also give some factorization theorems of Blaschke products...

Algebra of bounded analytic functions | Primary ideal | Carleson–Newman Blaschke product | Interpolating Blaschke product | Carleson-Newman Blaschke product

Algebra of bounded analytic functions | Primary ideal | Carleson–Newman Blaschke product | Interpolating Blaschke product | Carleson-Newman Blaschke product

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 361, Issue 2, pp. 492 - 505

... (as defined by Shields and Williams) and obtain new results regarding the membership of the derivative of a Blaschke product or a general inner function in such spaces...

Weighted Bergman spaces | Blaschke products | Normal weights | Interpolating sequences | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRABILITY | STOLZ | INNER FUNCTIONS | DUALITY | OPERATORS | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Weighted Bergman spaces | Blaschke products | Normal weights | Interpolating sequences | MATHEMATICS | MATHEMATICS, APPLIED | INTEGRABILITY | STOLZ | INNER FUNCTIONS | DUALITY | OPERATORS | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Journal Article

Kodai mathematical journal, ISSN 0386-5991, 2011, Volume 34, Issue 1, pp. 124 - 131

Let B be a Blaschke product with zeros {an}. If B′ ∈ Apα for certain p and α, it is shown that Σn (1 - |an|)β < ∞ for appropriate values...

Bergman space | uniformly discrete | Blaschke product | uniformly separated | separated | interpolating sequence | Hardy space | Interpolating sequence | Uniformly discrete | Separated | Uniformly separated | MATHEMATICS | INNER FUNCTIONS

Bergman space | uniformly discrete | Blaschke product | uniformly separated | separated | interpolating sequence | Hardy space | Interpolating sequence | Uniformly discrete | Separated | Uniformly separated | MATHEMATICS | INNER FUNCTIONS

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 10/2007, Volume 50, Issue 3, pp. 673 - 687

We study the membership of derivatives of Blaschke products in Hardy and Bergman spaces, especially for the the interpolating Blaschke products and for those whose zeros lie in a Stolz domain...

spaces | Stolz angle | Blaschke products | Bergman spaces | Interpolating sequences | Hardy spaces | interpolating sequences | MATHEMATICS | hardy spaces | bergman spaces | ANALYTIC FUNCTIONS | stolz angle | SPACES | INNER FUNCTIONS | Q(p) spaces

spaces | Stolz angle | Blaschke products | Bergman spaces | Interpolating sequences | Hardy spaces | interpolating sequences | MATHEMATICS | hardy spaces | bergman spaces | ANALYTIC FUNCTIONS | stolz angle | SPACES | INNER FUNCTIONS | Q(p) spaces

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 4/2011, Volume 24, Issue 1, pp. 49 - 57

We prove that if G is an analytic function in the unit disc such that G(z)→∞, as z→1, and B is an infinite Blaschke product whose sequence of zeros is contained in a Stolz angle with vertex at 1 then the function f...

Outer function | 30D40 | Mathematics | Topology | 30J45 | 30D45 | Geometry | Normal function | Bloch function | Mean Lipschitz spaces | Algebra | Analysis | Blaschke product | Mathematics, general | Applications of Mathematics | Interpolating Blaschke sequence | Thin Blaschke product | Interpolating blaschke sequence | Mean lipschitz spaces | Thin blaschke product | MATHEMATICS, APPLIED | SPACES | ANALYTIC-FUNCTIONS | MATHEMATICS | GROWTH | SETS | BOUNDED MEAN-OSCILLATION

Outer function | 30D40 | Mathematics | Topology | 30J45 | 30D45 | Geometry | Normal function | Bloch function | Mean Lipschitz spaces | Algebra | Analysis | Blaschke product | Mathematics, general | Applications of Mathematics | Interpolating Blaschke sequence | Thin Blaschke product | Interpolating blaschke sequence | Mean lipschitz spaces | Thin blaschke product | MATHEMATICS, APPLIED | SPACES | ANALYTIC-FUNCTIONS | MATHEMATICS | GROWTH | SETS | BOUNDED MEAN-OSCILLATION

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 08/2018, Volume 90, Issue 4, p. 1

.../10.1007/s00020-018-2451-9 Given an interpolating Blaschke product B with zeros .sub.j\{aj}, we seek to characterize the sequences of values...

Model subspaces | Interpolating Blaschke product | Inner function | Hardy spaces

Model subspaces | Interpolating Blaschke product | Inner function | Hardy spaces

Journal Article

10.
Full Text
A New Class of Inner Functions Uniformly Approximable by Interpolating Blaschke Products

Complex Analysis and Operator Theory, ISSN 1661-8254, 3/2011, Volume 5, Issue 1, pp. 219 - 235

...)}}$$ on the corona of H ∞ and show that these functions are uniformly approximable by interpolating Blaschke products.

Maximal ideal space | Operator Theory | Primary 30D50 | Secondary 46J15 | Interpolating Blaschke products | Inner functions | Analysis | Uniform approximation | Zero sets | Mathematics, general | Quotient algebras by inner functions | Mathematics | GLEASON PARTS | MATHEMATICS, APPLIED | H-INFINITY | DIVISION | MATHEMATICS | DOUGLAS ALGEBRAS | STABLE RANK

Maximal ideal space | Operator Theory | Primary 30D50 | Secondary 46J15 | Interpolating Blaschke products | Inner functions | Analysis | Uniform approximation | Zero sets | Mathematics, general | Quotient algebras by inner functions | Mathematics | GLEASON PARTS | MATHEMATICS, APPLIED | H-INFINITY | DIVISION | MATHEMATICS | DOUGLAS ALGEBRAS | STABLE RANK

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 05/2012, Volume 262, Issue 9, pp. 3749 - 3774

...–Newman Blaschke product and h∈H∞ is an invertible function. We use this result to show that, except for finite Blaschke products, no inner function in the little Bloch space is in the closure of one of these components...

Inner functions | Carleson–Newman Blaschke products | Connected components | Carleson-Newman Blaschke products | GLEASON PARTS | RATIOS | GENERATE H-INFINITY | APPROXIMATION | INVARIANT CONNECTED COMPONENTS | DIVISION | BOUNDED ANALYTIC-FUNCTIONS | MATHEMATICS | ALGEBRAS | INTERPOLATING BLASCHKE PRODUCTS | STABLE RANK | Algebra

Inner functions | Carleson–Newman Blaschke products | Connected components | Carleson-Newman Blaschke products | GLEASON PARTS | RATIOS | GENERATE H-INFINITY | APPROXIMATION | INVARIANT CONNECTED COMPONENTS | DIVISION | BOUNDED ANALYTIC-FUNCTIONS | MATHEMATICS | ALGEBRAS | INTERPOLATING BLASCHKE PRODUCTS | STABLE RANK | Algebra

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 6/2016, Volume 16, Issue 2, pp. 243 - 263

... Carleson–Newman Blaschke product b.

Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Closed ideal | Finitely generated ideal | Mathematics | Douglas algebra | Gleason part | Primary 30H50 | 46J20 | Carleson–Newman Blaschke product | Secondary 30J10 | 30H05 | Analysis | 46J15 | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | INTERPOLATING BLASCHKE PRODUCTS | Carleson-Newman Blaschke product | H-INFINITY

Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Closed ideal | Finitely generated ideal | Mathematics | Douglas algebra | Gleason part | Primary 30H50 | 46J20 | Carleson–Newman Blaschke product | Secondary 30J10 | 30H05 | Analysis | 46J15 | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | INTERPOLATING BLASCHKE PRODUCTS | Carleson-Newman Blaschke product | H-INFINITY

Journal Article

Constructive Approximation, ISSN 0176-4276, 6/2012, Volume 35, Issue 3, pp. 345 - 361

... order.In 2010, the second author proposed a unit disc analog of Bank’s first result. In the analog, {z n } is a sparse Blaschke sequence and A(z) belongs to the Korenblum space. The aim of the present paper is to introduce unit disc analogs of the two remaining results due to Bank and Sauer.

Exponential sequence | 34C10 | Oscillation theory | Blaschke-oscillatory | Uniformly separated sequence | 30J10 | Mathematics | 34M10 | 46B70 | Numerical Analysis | Analysis | Blaschke product | Logarithmic derivative | Prescribed zero sequence | MATHEMATICS | INTERPOLATING BLASCHKE PRODUCTS | GROWTH | EQUATIONS | Banks (Finance)

Exponential sequence | 34C10 | Oscillation theory | Blaschke-oscillatory | Uniformly separated sequence | 30J10 | Mathematics | 34M10 | 46B70 | Numerical Analysis | Analysis | Blaschke product | Logarithmic derivative | Prescribed zero sequence | MATHEMATICS | INTERPOLATING BLASCHKE PRODUCTS | GROWTH | EQUATIONS | Banks (Finance)

Journal Article

Analysis, ISSN 0174-4747, 10/2007, Volume 27, Issue 2, pp. 261 - 272

...–| ) in terms of the zeros of the underlying interpolating Blaschke product . We use our formula to show that for every interpolating Blaschke product there exists another...

orthogonality | Interpolating Blaschke products | combinatorial identity

orthogonality | Interpolating Blaschke products | combinatorial identity

Journal Article

Kodai mathematical journal, ISSN 0386-5991, 2004, Volume 27, Issue 3, pp. 354 - 359

If B is a Blaschke product with zeros {an} and if ∑n(1−|an|)α is finite for some α∈(1/2, 1], then limits are found on the rate of growth...

Bergman space | Blaschke product | interpolating sequence | Hardy space

Bergman space | Blaschke product | interpolating sequence | Hardy space

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2012, Volume 388, Issue 2, pp. 1013 - 1026

Motivated by the Invariant Subspace Problem, we describe explicitly the closed subspace H generated by the limit points in the H norm of the orbit of a thin Blaschke product B under composition...

Invariant subspaces | Eigenfunctions of composition operators | Blaschke products | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | INTERPOLATING-SEQUENCES

Invariant subspaces | Eigenfunctions of composition operators | Blaschke products | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | INTERPOLATING-SEQUENCES

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 2/2019, Volume 13, Issue 1, pp. 45 - 59

.... A criterion for an interpolating Blaschke product to be in the closures is given. We also consider the relation between the closures and the space of bounded analytic...

46E15 | Operator Theory | Closure | Interpolating Blaschke product | Analysis | Dirichlet type spaces | Mathematics, general | 30J10 | Mathematics | The Bloch space | 30H30 | MATHEMATICS | MATHEMATICS, APPLIED | CARLESON MEASURES | MULTIPLIERS | OPERATORS | ANALYTIC-FUNCTIONS | FAMILY

46E15 | Operator Theory | Closure | Interpolating Blaschke product | Analysis | Dirichlet type spaces | Mathematics, general | 30J10 | Mathematics | The Bloch space | 30H30 | MATHEMATICS | MATHEMATICS, APPLIED | CARLESON MEASURES | MULTIPLIERS | OPERATORS | ANALYTIC-FUNCTIONS | FAMILY

Journal Article

Kyushu journal of mathematics, ISSN 1340-6116, 2016, Volume 70, Issue 2, pp. 259 - 266

We introduce several topics for sequences in the unit disc of the complex plane and the space of bounded analytic functions. We characterize sequences that are...

Carleson condition | Blaschke product | bounded analytic function | zero sequence | interpolating sequence | Bounded analytic function | Interpolating sequence | Zero sequence | MATHEMATICS

Carleson condition | Blaschke product | bounded analytic function | zero sequence | interpolating sequence | Bounded analytic function | Interpolating sequence | Zero sequence | MATHEMATICS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2000, Volume 128, Issue 6, pp. 1799 - 1806

Journal Article

JOURNAL OF FUNCTIONAL ANALYSIS, ISSN 0022-1236, 04/2011, Volume 260, Issue 7, pp. 2086 - 2147

Let H-infinity be the Banach algebra of bounded analytic functions on the open unit disk D. Let G be the union set of all nontrivial Gleason parts in the...

Algebra of bounded analytic functions | GLEASON PARTS | MATHEMATICS | Interpolating Blaschke product | Ideal theory | Carleson-Newman Blaschke product | BOUNDED ANALYTIC FUNCTIONS | Big disk algebra | Gleason part | DOUGLAS ALGEBRAS

Algebra of bounded analytic functions | GLEASON PARTS | MATHEMATICS | Interpolating Blaschke product | Ideal theory | Carleson-Newman Blaschke product | BOUNDED ANALYTIC FUNCTIONS | Big disk algebra | Gleason part | DOUGLAS ALGEBRAS

Journal Article

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