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...

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

Journal of Difference Equations and Applications, ISSN 1023-6198, 09/2017, Volume 23, Issue 9, pp. 1584 - 1596

It is well known that the bounding curve of the central hyperbolic component of the Multibrot set in the parameter space of unicritical degree d polynomials is...

Blaschke product | parameter space | epicycloid | Secondary: 37F10 | Primary: 30D05 | MATHEMATICS, APPLIED | Functions (mathematics) | Polynomials | Cusps | Mathematical analysis | Epicycloids

Blaschke product | parameter space | epicycloid | Secondary: 37F10 | Primary: 30D05 | MATHEMATICS, APPLIED | Functions (mathematics) | Polynomials | Cusps | Mathematical analysis | Epicycloids

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...

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

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 2, pp. 1163 - 1196

LetΓ=def{(z+w,zw):|z|≤1,|w|≤1}⊂C2. A Γ-inner function is a holomorphic map h from the unit disc D to Γ whose boundary values at almost all points of the unit...

Pick matrix | Blaschke product | Interpolation | Complex geodesic | Symmetrized bidisc | MATHEMATICS, APPLIED | NEVANLINNA-PICK INTERPOLATION | THEOREM | COMPLEX GEODESICS | POLYDISK | BOUNDARY INTERPOLATION | AUTOMORPHISMS | CONTRACTIONS | MATHEMATICS | DIMENSIONS | EXTREMAL HOLOMORPHIC MAPS | Mathematics - Complex Variables

Pick matrix | Blaschke product | Interpolation | Complex geodesic | Symmetrized bidisc | MATHEMATICS, APPLIED | NEVANLINNA-PICK INTERPOLATION | THEOREM | COMPLEX GEODESICS | POLYDISK | BOUNDARY INTERPOLATION | AUTOMORPHISMS | CONTRACTIONS | MATHEMATICS | DIMENSIONS | EXTREMAL HOLOMORPHIC MAPS | Mathematics - Complex Variables

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2013, Volume 241, pp. 58 - 78

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...

Schwarz lemma | Bounded analytic functions | Extremal problems | Blaschke products | Bergman spaces | MATHEMATICS | INVARIANT SUBSPACES | LEMMA | SETS | EXTENSION

Schwarz lemma | Bounded analytic functions | Extremal problems | Blaschke products | Bergman spaces | MATHEMATICS | INVARIANT SUBSPACES | LEMMA | SETS | EXTENSION

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2017, Volume 516, pp. 186 - 211

Let B be a degree-n Blaschke product and, for λ∈T, let z1,λ,…,zn,λ, ordered according to increasing argument, denote the (distinct) solutions to B(z)−λ=0. Then...

Ellipse | Numerical range | Blaschke products | Poncelet curve | Iterate | Composition operator | Disk automorphism | MATHEMATICS, APPLIED | INNER FUNCTIONS | ELLIPSES | MATHEMATICS | OPERATOR | MATRICES | ELLIPTIC DISC

Ellipse | Numerical range | Blaschke products | Poncelet curve | Iterate | Composition operator | Disk automorphism | MATHEMATICS, APPLIED | INNER FUNCTIONS | ELLIPSES | MATHEMATICS | OPERATOR | MATRICES | ELLIPTIC DISC

Journal Article

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

We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic...

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). The envelope of the family of lines...

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

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 2, pp. 1419 - 1434

We address the question: Are the inner functions in the uniform closure in H∞ of the indestructible Blaschke products? We show, in particular, that every inner...

Indestructible | Blaschke product | Inner function | Singular inner function | MATHEMATICS | MATHEMATICS, APPLIED

Indestructible | Blaschke product | Inner function | Singular inner function | MATHEMATICS | MATHEMATICS, APPLIED

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...

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

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2017, Volume 37, Issue 7, pp. 3567 - 3585

The goal of this paper is to study the family of singular perturbations of Blaschke products given by B-a,B- lambda(z) = z(3) z-a/1-az +lambda/z(2). We focus...

Singular perturbations | Blaschke products | Connectivity of Fatou components | Holomorphic dynamics | McMullen-like Julia sets | MATHEMATICS | singular perturbations | MATHEMATICS, APPLIED | connectivity of Fatou components | PERTURBED RATIONAL MAPS | DYNAMICS | MCMULLEN MAPS | FAMILY

Singular perturbations | Blaschke products | Connectivity of Fatou components | Holomorphic dynamics | McMullen-like Julia sets | MATHEMATICS | singular perturbations | MATHEMATICS, APPLIED | connectivity of Fatou components | PERTURBED RATIONAL MAPS | DYNAMICS | MCMULLEN MAPS | FAMILY

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2015, Volume 277, pp. 106 - 114

In this paper, we study a special kind of finite Blaschke products called Chebyshev–Blaschke products fn,τ which can be defined by the Jacobi cosine function...

Zolotarev’s problem | Finite Blaschke products | Ritt’s theorems | Least deviation from zero | Chebyshev polynomials | Zolotarev's problem | Ritt's theorems | MATHEMATICS, APPLIED | Differential equations

Zolotarev’s problem | Finite Blaschke products | Ritt’s theorems | Least deviation from zero | Chebyshev polynomials | Zolotarev's problem | Ritt's theorems | MATHEMATICS, APPLIED | Differential equations

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 365, Issue 1, pp. 93 - 102

By connecting Blaschke products, unitary dilations of matrices, numerical range, Poncelet's theorem and interpolation, we extend and simplify Gau and Wu's work...

Sendov's conjecture | Blaschke product | Numerical range | Poncelet curve | Unitary dilation | MATHEMATICS | MATHEMATICS, APPLIED | NORMAL COMPRESSION | POLYGONS | CURVES

Sendov's conjecture | Blaschke product | Numerical range | Poncelet curve | Unitary dilation | MATHEMATICS | MATHEMATICS, APPLIED | NORMAL COMPRESSION | POLYGONS | CURVES

Journal Article

Computational Methods and Function Theory, ISSN 1617-9447, 3/2019, Volume 19, Issue 1, pp. 173 - 182

For any finite Blaschke product B, there is an injective analytic map $$\varphi :{\mathbb {D}}\rightarrow {\mathbb {C}}$$ φ : D → C and a polynomial p of the...

30C10 | Computational Mathematics and Numerical Analysis | Blaschke products | Fingerprints | Functions of a Complex Variable | Analysis | Primary 30J10 | Mathematics | Polynomials | Conformal models | Secondary 30C35 | MATHEMATICS | MATHEMATICS, APPLIED | EQUIVALENCE

30C10 | Computational Mathematics and Numerical Analysis | Blaschke products | Fingerprints | Functions of a Complex Variable | Analysis | Primary 30J10 | Mathematics | Polynomials | Conformal models | Secondary 30C35 | MATHEMATICS | MATHEMATICS, APPLIED | EQUIVALENCE

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...

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

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

Publicacions Matemàtiques, ISSN 0214-1493, 1/2015, Volume 59, Issue 1, pp. 45 - 54

For a Nevanlinna-Pick problem with more than one solution, Rolf Nevanlinna proved that all extremal solutions are inner functions. If the interpolation points...

Analytic functions | Interpolation | Mathematical theorems | Blaschke product | Logarithmic capacity | Minimal interpolation | Logarithmic capacit | MATHEMATICS | minimal interpolation | logarithmic capacity | 30E05 | 30J10 | Blaschke products

Analytic functions | Interpolation | Mathematical theorems | Blaschke product | Logarithmic capacity | Minimal interpolation | Logarithmic capacit | MATHEMATICS | minimal interpolation | logarithmic capacity | 30E05 | 30J10 | Blaschke products

Journal Article

Studia Scientiarum Mathematicarum Hungarica, ISSN 0081-6906, 06/2013, Volume 50, Issue 2, pp. 159 - 198

Let K subset of R-2 be an o-symmetric convex body, and K* its polar body. Then we have vertical bar K vertical bar.vertical bar K*vertical bar >= 8, with...

Primary 52A40 | Santaló point | Blaschke-Santaló inequality | Banach-Mazur distance | reverse Blaschke-Santaló inequality | Secondary 52A38, 52A10 | stability | lower estimates | volume product in the plane | PROOF | ZONOIDS | VERSIONS | Santalo point | Blaschke-Santalo inequality | CONCAVE FUNCTIONS | INTEGRALS | MATHEMATICS | BANACH-SPACES | reverse Blaschke-Santalo inequality | MAHLERS CONJECTURE | Inequalities (Mathematics) | Convex sets | Research | Mathematical research | Estimates

Primary 52A40 | Santaló point | Blaschke-Santaló inequality | Banach-Mazur distance | reverse Blaschke-Santaló inequality | Secondary 52A38, 52A10 | stability | lower estimates | volume product in the plane | PROOF | ZONOIDS | VERSIONS | Santalo point | Blaschke-Santalo inequality | CONCAVE FUNCTIONS | INTEGRALS | MATHEMATICS | BANACH-SPACES | reverse Blaschke-Santalo inequality | MAHLERS CONJECTURE | Inequalities (Mathematics) | Convex sets | Research | Mathematical research | Estimates

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

2013, 2013, Fields Institute Communications, ISBN 9781489990822, Volume 65, 323

?Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields...

Mathematics | Blaschke products | Analytic functions | Difference and Functional Equations | Functional Analysis | Functions of a Complex Variable

Mathematics | Blaschke products | Analytic functions | Difference and Functional Equations | Functional Analysis | Functions of a Complex Variable

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