Dynamical Systems, ISSN 1468-9367, 01/2016, Volume 31, Issue 1, pp. 89 - 105

.... Our main example is Blaschke products, for which we provide rigorous error estimates on the difference between Birkhoff density and the superstatistical approximation.

Blaschke product | superstatistics | invariant density | MATHEMATICS, APPLIED | SYSTEMS | TURBULENCE | PHYSICS, MATHEMATICAL | GENERALIZED STATISTICAL-MECHANICS | ENTROPY | Errors | Maps | Approximation | Dynamics | Mathematical analysis | Estimates | Density | Invariants

Blaschke product | superstatistics | invariant density | MATHEMATICS, APPLIED | SYSTEMS | TURBULENCE | PHYSICS, MATHEMATICAL | GENERALIZED STATISTICAL-MECHANICS | ENTROPY | Errors | Maps | Approximation | Dynamics | Mathematical analysis | Estimates | Density | Invariants

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2018, Volume 467, Issue 1, pp. 711 - 722

For a Blaschke product B of degree d and λ on ∂D, let ℓλ be the set of lines joining each distinct two preimages in B−1(λ...

Blaschke product | Dual curve | Algebraic curve | Complex analysis | ELLIPSES | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL RANGE | MATRICES | Mathematics - Complex Variables

Blaschke product | Dual curve | Algebraic curve | Complex analysis | ELLIPSES | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL RANGE | MATRICES | Mathematics - Complex Variables

Journal Article

Nonlinearity, ISSN 0951-7715, 09/2016, Volume 29, Issue 11, pp. 3464 - 3495

The goal of this paper is to investigate the family of Blasche products B-a(z) = z(3) z-a/1-(a) over barz , which is a rational family of perturbations of the doubling map...

circle maps | Blaschke products | tongues | holomorphic dynamics | MATHEMATICS, APPLIED | SET | DOUBLE-STANDARD MAPS | BIFURCATIONS | PHYSICS, MATHEMATICAL | CIRCLE | FAMILY | DYNAMICS | ARNOLD TONGUES | TIP | Mathematics - Dynamical Systems | Dinàmica topològica | Topological dynamics | Differentiable dynamical systems | Sistemes dinàmics diferenciables

circle maps | Blaschke products | tongues | holomorphic dynamics | MATHEMATICS, APPLIED | SET | DOUBLE-STANDARD MAPS | BIFURCATIONS | PHYSICS, MATHEMATICAL | CIRCLE | FAMILY | DYNAMICS | ARNOLD TONGUES | TIP | Mathematics - Dynamical Systems | Dinàmica topològica | Topological dynamics | Differentiable dynamical systems | Sistemes dinàmics diferenciables

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2010, Volume 138, Issue 6, pp. 2113 - 2123

Let R be a finite Blaschke product of degree at least two with R(0)=0. Then there exists a relation between the associated composition operator C_R on the Hardy space and the C^*-algebra \mathcal {O}_R (J_R...

Algebra | Mathematical theorems | Quotients | Julia sets | Adjoints | Hilbert spaces | Mathematical functions | Dynamical systems | Operator theory | Blaschke product | Complex dynamical system | C- algebra | Toeplitz operator | Composition operator | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | ADJOINTS | complex dynamical system | C-algebra

Algebra | Mathematical theorems | Quotients | Julia sets | Adjoints | Hilbert spaces | Mathematical functions | Dynamical systems | Operator theory | Blaschke product | Complex dynamical system | C- algebra | Toeplitz operator | Composition operator | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | ADJOINTS | complex dynamical system | C-algebra

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 1755-1633, 2012, Volume 85, Issue 2, pp. 315 - 324

The Blaschke–Petkantschin formula is a geometric measure decomposition of the -fold product of Lebesgue measure on ℝ...

polar decomposition | co-area formula | moments of Gaussian determinant | Blaschke-Petkantschin formula | MATHEMATICS

polar decomposition | co-area formula | moments of Gaussian determinant | Blaschke-Petkantschin formula | MATHEMATICS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2020, Volume 148, Issue 1, pp. 193 - 201

For an infinite Blaschke product B, does there necessarily exist \delta >0 such that each w satisfying \vert w\vert...

MATHEMATICS | Blaschke product | MATHEMATICS, APPLIED | CAUCHY TRANSFORMS | Blaschke condition | infinite range

MATHEMATICS | Blaschke product | MATHEMATICS, APPLIED | CAUCHY TRANSFORMS | Blaschke condition | infinite range

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

Analysis and Mathematical Physics, ISSN 1664-2368, 3/2019, Volume 9, Issue 1, pp. 221 - 249

The determination of a finite Blaschke product from its critical points is a well-known problem with interrelations to several other topics...

30E05 | 30J10 | Mathematics | Critical point | Stieltjes polynomial | Equilibrium | Mathematical Methods in Physics | Van Vleck polynomial | Analysis | Blaschke product | Moment problem | 26C15 | Electrostatics | MATHEMATICS | MATHEMATICS, APPLIED

30E05 | 30J10 | Mathematics | Critical point | Stieltjes polynomial | Equilibrium | Mathematical Methods in Physics | Van Vleck polynomial | Analysis | Blaschke product | Moment problem | 26C15 | Electrostatics | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

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

Journal of Functional Analysis, ISSN 0022-1236, 03/2017, Volume 272, Issue 6, pp. 2463 - 2486

For 1/2

Blaschke product | Inner function | Hardy space | MATHEMATICS | BESOV-SPACES | BLASCHKE PRODUCTS | DERIVATIVES

Journal Article

2018, ISBN 9783319782461, 340

This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis...

Mathematics | Functions of complex variables | Functional Analysis | Operator Theory

Mathematics | Functions of complex variables | Functional Analysis | Operator Theory

eBook

Computational Methods and Function Theory, ISSN 1617-9447, 6/2015, Volume 15, Issue 2, pp. 277 - 287

.... We give a characterization of finite Blaschke products via the boundary behaviour of a weighted local hyperbolic distortion of an analytic self-map of the unit disk.

Angular derivative | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Hyperbolic distortion | 30H05 | Analysis | 30D40 | Boundary regularity | 30J10 | Mathematics | Finite Blaschke product | 30F45 | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | MAPS | SPACES | ANALYTIC-FUNCTIONS

Angular derivative | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Hyperbolic distortion | 30H05 | Analysis | 30D40 | Boundary regularity | 30J10 | Mathematics | Finite Blaschke product | 30F45 | MATHEMATICS | MATHEMATICS, APPLIED | COMPOSITION OPERATORS | MAPS | SPACES | ANALYTIC-FUNCTIONS

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 8/2013, Volume 13, Issue 2, pp. 253 - 262

We prove that the composition of two indestructible Blaschke products is again an indestructible Blaschke product...

Computational Mathematics and Numerical Analysis | Blaschke products | Functions of a Complex Variable | 30H05 | Analysis | 30J05 | Semigroups | 30J10 | Mathematics | Bounded analytic functions | MATHEMATICS | MATHEMATICS, APPLIED | SETS | INNER FUNCTIONS | ANALYTIC-FUNCTIONS

Computational Mathematics and Numerical Analysis | Blaschke products | Functions of a Complex Variable | 30H05 | Analysis | 30J05 | Semigroups | 30J10 | Mathematics | Bounded analytic functions | MATHEMATICS | MATHEMATICS, APPLIED | SETS | INNER FUNCTIONS | ANALYTIC-FUNCTIONS

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 03/2014, Volume 57, Issue 1, pp. 80 - 89

We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products...

Disk algebra | Jacobson radical | Semicrossed product | MATHEMATICS | BLASCHKE PRODUCTS | disk algebra | semicrossed product | Mathematics - Operator Algebras

Disk algebra | Jacobson radical | Semicrossed product | MATHEMATICS | BLASCHKE PRODUCTS | disk algebra | semicrossed product | Mathematics - Operator Algebras

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2015, Volume 426, Issue 2, pp. 1201 - 1216

We present four algorithms to determine whether or not a Blaschke product is a composition of two non-trivial Blaschke products and, if it is, the algorithms suggest what the composition must...

Blaschke product | Critical values | Composition | Poncelet curve | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL RANGE | INNER FUNCTIONS | POLYGONS | Algorithms

Blaschke product | Critical values | Composition | Poncelet curve | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL RANGE | INNER FUNCTIONS | POLYGONS | Algorithms

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 10/2009, Volume 52, Issue 3, pp. 689 - 705

We study the membership of Blaschke products in Lipschitz spaces, especially for interpolating Blaschke products and for those whose zeros lie in a Stolz angle...

Bergman space | Lipschitz space | Blaschke products | Hardy space | MATHEMATICS | Geometry | Theorems | Mathematics

Bergman space | Lipschitz space | Blaschke products | Hardy space | MATHEMATICS | Geometry | Theorems | Mathematics

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

Constructive Approximation, ISSN 0176-4276, 1/2008, Volume 27, Issue 1, pp. 75 - 98

..., ..., wn on the unit circle, we show how to construct a Blaschke product B of degree n such that B...

Numerical Analysis | Analysis | Mathematics | Blaschke product | Sendov's conjecture | Lagrange interpolation | Newton interpolation method | MATHEMATICS | LAGRANGE

Numerical Analysis | Analysis | Mathematics | Blaschke product | Sendov's conjecture | Lagrange interpolation | Newton interpolation method | MATHEMATICS | LAGRANGE

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 2, pp. 1354 - 1366

We provide a new proof of a theorem of Fujimura characterizing Blaschke products of degree-4 that are compositions of two degree-2 Blaschke products, connect this result to the numerical ranges...

Blaschke product | Numerical range | Compression of the shift operator | Poncelet curve | MATHEMATICS | MATHEMATICS, APPLIED | POLYGONS

Blaschke product | Numerical range | Compression of the shift operator | Poncelet curve | MATHEMATICS | MATHEMATICS, APPLIED | POLYGONS

Journal Article

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, ISSN 1239-629X, 2019, Volume 44, Issue 1, pp. 569 - 580

...). We give a sufficient condition for a Blaschke product with zeros in a Stolz domain to be a one- component inner function...

Bergman space | MATHEMATICS | SPACES | Blaschke product | HARDY | singular inner function | BLASCHKE PRODUCTS | DERIVATIVES | Hardy space | one-component inner function

Bergman space | MATHEMATICS | SPACES | Blaschke product | HARDY | singular inner function | BLASCHKE PRODUCTS | DERIVATIVES | Hardy space | one-component inner function

Journal Article

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