数学学报：英文版, ISSN 1439-8516, 2014, Volume 30, Issue 3, pp. 499 - 504

For a rectifable Jordan curve Γ with complementary domainsD and D,Anderson conjectured that the Faber operator is a bounded isomorphism between the Besov...

操作 | 安德森 | 注记 | 麦 | Besov空间 | 解析函数 | 嘉华 | Jordan曲线 | Grunsky operator | 46E15 | Faber operator | 30E10 | 47B38 | Mathematics, general | Mathematics | quasi-circle | Besov space | Hilbert operator | MATHEMATICS | MATHEMATICS, APPLIED | SETS

操作 | 安德森 | 注记 | 麦 | Besov空间 | 解析函数 | 嘉华 | Jordan曲线 | Grunsky operator | 46E15 | Faber operator | 30E10 | 47B38 | Mathematics, general | Mathematics | quasi-circle | Besov space | Hilbert operator | MATHEMATICS | MATHEMATICS, APPLIED | SETS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 2/2018, Volume 12, Issue 2, pp. 325 - 354

Let $$\Gamma $$ Γ be a bounded Jordan curve with complementary components $$\Omega ^{\pm }$$ Ω± . We show that the jump decomposition is an isomorphism if and...

Bergman space | Grunsky operator | Quasicircles | 30C62 | Dirichlet space | Primary 30F15 | Mathematics | Secondary 30C55 | 31C25 | Quasiconformal extension | 31C05 | Operator Theory | Jump decomposition | Faber polynomials | 35Q15 | Analysis | Mathematics, general | Schiffer operator | MATHEMATICS | MATHEMATICS, APPLIED | Naturvetenskap | Natural Sciences

Bergman space | Grunsky operator | Quasicircles | 30C62 | Dirichlet space | Primary 30F15 | Mathematics | Secondary 30C55 | 31C25 | Quasiconformal extension | 31C05 | Operator Theory | Jump decomposition | Faber polynomials | 35Q15 | Analysis | Mathematics, general | Schiffer operator | MATHEMATICS | MATHEMATICS, APPLIED | Naturvetenskap | Natural Sciences

Journal Article

Constructive Approximation, ISSN 0176-4276, 4/2018, Volume 47, Issue 2, pp. 211 - 235

By exploiting a link between Bergman orthogonal polynomials and the Grunsky matrix, probably first observed by Kühnau (Ann Acad Sci Math 10:313–329, 1985), we...

30C10 | Bergman orthogonal polynomials | Bergman shift | 30E10 | 30C62 | Grunsky matrix | Mathematics | Faber polynomials | Conformal mapping | Numerical Analysis | Analysis | 41A10 | 65E05 | Quasiconformal mapping | MATHEMATICS | OPERATOR | ASYMPTOTICS | DOMAINS

30C10 | Bergman orthogonal polynomials | Bergman shift | 30E10 | 30C62 | Grunsky matrix | Mathematics | Faber polynomials | Conformal mapping | Numerical Analysis | Analysis | 41A10 | 65E05 | Quasiconformal mapping | MATHEMATICS | OPERATOR | ASYMPTOTICS | DOMAINS

Journal Article

Complex Variables and Elliptic Equations: Complex Analysis and Potential Theory, in memory of Promarz M. Tamrazov, ISSN 1747-6933, 01/2014, Volume 59, Issue 1, pp. 48 - 58

We establish the underlying quasiconformal features of the generalized Grunsky coefficients and provide their applications to qualitative and quantitative...

Grunsky operator | quadratic differential | complex homotopy | quasiconformal extension | Primary: 30C15 | Secondary: 30F60 | univalent function | MATHEMATICS | INEQUALITIES | COEFFICIENT CONDITIONS | GEOMETRY | Complex variables

Grunsky operator | quadratic differential | complex homotopy | quasiconformal extension | Primary: 30C15 | Secondary: 30F60 | univalent function | MATHEMATICS | INEQUALITIES | COEFFICIENT CONDITIONS | GEOMETRY | Complex variables

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 12/2009, Volume 3, Issue 4, pp. 835 - 846

We establish several conditions which are equivalent to $$|[Bx,x]| \leq \langle Ax, x \rangle,\quad \forall x \in {{\mathcal{H}}}$$ , where A is a nonnegative...

selfadjoint operators | Complex symmetric operator | Operator Theory | complex symmetric matrix | Analysis | hermitian-symmetric inequalities | Mathematics, general | 47B99 | Mathematics | hermitian operators | bilinear form | Grunsky inequality | Hermitian operators | Selfadjoint operators | Complex symmetric matrix | Bilinear form | Hermitian-symmetric inequalities | MATHEMATICS | MATHEMATICS, APPLIED | PLANAR DOMAIN | FRIEDRICHS OPERATOR

selfadjoint operators | Complex symmetric operator | Operator Theory | complex symmetric matrix | Analysis | hermitian-symmetric inequalities | Mathematics, general | 47B99 | Mathematics | hermitian operators | bilinear form | Grunsky inequality | Hermitian operators | Selfadjoint operators | Complex symmetric matrix | Bilinear form | Hermitian-symmetric inequalities | MATHEMATICS | MATHEMATICS, APPLIED | PLANAR DOMAIN | FRIEDRICHS OPERATOR

Journal Article

Acta Mathematica Sinica, English Series, ISSN 1439-8516, 4/2014, Volume 30, Issue 4, pp. 591 - 600

Being a Strebel point gives a sufficient condition for that the extremal Beltrami coefficient is uniquely determined in a Teichmüller equivalence class. We...

Mathematics, general | Mathematics | Quasiconformal mappings | Strebel points | Grunsky inequalities | 30F60 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Studies | Theorems | Applied mathematics | matmod

Mathematics, general | Mathematics | Quasiconformal mappings | Strebel points | Grunsky inequalities | 30F60 | MATHEMATICS | MATHEMATICS, APPLIED | INEQUALITIES | Studies | Theorems | Applied mathematics | matmod

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2017, Volume 11, Issue 7, pp. 1491 - 1501

One of the long-standing problems in the quasiconformal theory is finding sharp distortion bounds for k-quasiconformal maps for arbitrary $$k <1$$ k < 1 . We...

30C75 | 30F60 | 30C62 | Infinite dimensional holomorphy | Complex geodesic | Mathematics | 32F45 | Variational problem | Functional | Secondary: 30F45 | Operator Theory | Primary: 30C55 | Invariant metrics | 46G20 | Analysis | Univalent | Mathematics, general | Teichmüller space | Grunsky inequalities | Quasiconformal | MATHEMATICS, APPLIED | MATHEMATICS | Teichmuller space | COEFFICIENT | MAPPINGS

30C75 | 30F60 | 30C62 | Infinite dimensional holomorphy | Complex geodesic | Mathematics | 32F45 | Variational problem | Functional | Secondary: 30F45 | Operator Theory | Primary: 30C55 | Invariant metrics | 46G20 | Analysis | Univalent | Mathematics, general | Teichmüller space | Grunsky inequalities | Quasiconformal | MATHEMATICS, APPLIED | MATHEMATICS | Teichmuller space | COEFFICIENT | MAPPINGS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 12/2015, Volume 9, Issue 8, pp. 1663 - 1679

Tietz defined a generalization of Faber polynomials for conformal maps into a compact Riemann surface, which we will call the Faber–Tietz functions. We give a...

30B99 | Riemann surfaces | 30C55 | 30F30 | Faber series | Mathematics | Cauchy differential | 30C35 | Operator Theory | Faber polynomials | Analysis | Mathematics, general | Elliptic functions | Grunsky inequalities | MATHEMATICS | MATHEMATICS, APPLIED

30B99 | Riemann surfaces | 30C55 | 30F30 | Faber series | Mathematics | Cauchy differential | 30C35 | Operator Theory | Faber polynomials | Analysis | Mathematics, general | Elliptic functions | Grunsky inequalities | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Science in China Series A: Mathematics, ISSN 1006-9283, 12/2007, Volume 50, Issue 12, pp. 1805 - 1817

We discuss the holomorphic dependance and the compactness of the Grunsky operator for a univalent function.

47B07 | Grunsky operator | 30C55 | Hilbert-Schmidt operator | 30C62 | Mathematics | Applications of Mathematics | quasiconformal mapping | compact operator | univalent function | Compact operator | Univalent function | Quasiconformal mapping | MATHEMATICS, APPLIED | INEQUALITIES | UNIVERSAL TEICHMULLER SPACE | METRICS | COMPLEX-GEOMETRY | CIRCLE | MATHEMATICS | CURVE

47B07 | Grunsky operator | 30C55 | Hilbert-Schmidt operator | 30C62 | Mathematics | Applications of Mathematics | quasiconformal mapping | compact operator | univalent function | Compact operator | Univalent function | Quasiconformal mapping | MATHEMATICS, APPLIED | INEQUALITIES | UNIVERSAL TEICHMULLER SPACE | METRICS | COMPLEX-GEOMETRY | CIRCLE | MATHEMATICS | CURVE

Journal Article

Memoirs of the American Mathematical Society, ISSN 0065-9266, 09/2006, Volume 183, Issue 861, pp. 1 - 119

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2018, Volume 465, Issue 1, pp. 658 - 672

This paper deals with the p-integrable Teichmüller space and gives an intrinsic characterization of a p-integrable asymptotic affine homeomorphism for p>2....

Quasi-symmetric homeomorphism | Universal Teichmüller space | Quasiconformal mapping | p-integrable Teichmüller space | Besov space | WEIL-PETERSSON | MATHEMATICS, APPLIED | BMO | Universal Teichmuller space | EXTENSION | GRUNSKY OPERATOR | CIRCLE | QUASI-SYMMETRIC HOMEOMORPHISMS | MATHEMATICS | CONTRACTIBILITY | p-integrable Teichmuller space | EQUATION

Quasi-symmetric homeomorphism | Universal Teichmüller space | Quasiconformal mapping | p-integrable Teichmüller space | Besov space | WEIL-PETERSSON | MATHEMATICS, APPLIED | BMO | Universal Teichmuller space | EXTENSION | GRUNSKY OPERATOR | CIRCLE | QUASI-SYMMETRIC HOMEOMORPHISMS | MATHEMATICS | CONTRACTIBILITY | p-integrable Teichmuller space | EQUATION

Journal Article

12.
Full Text
Faber polynomials with applications to univalent functions with quasiconformal extensions

中国科学：数学英文版, ISSN 1674-7283, 2009, Issue 10, pp. 2121 - 2131

We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In...

univalent | mapping | quasiconformal | polynomial | function | Grunsky | Faber | operator

univalent | mapping | quasiconformal | polynomial | function | Grunsky | Faber | operator

Journal Article

2020, Volume 22, Issue 3

Consider a multiply-connected domain Sigma in the sphere bounded by n non-intersecting quasicircles. We characterize the Dirichlet space of Sigma as an...

Grunsky operator | Faber operator | Naturvetenskap | Matematisk analys | Faber series | quasicircles | Dirichlet spaces | Mathematics | Natural Sciences | Matematik | Mathematical Analysis | multiply-connected domains

Grunsky operator | Faber operator | Naturvetenskap | Matematisk analys | Faber series | quasicircles | Dirichlet spaces | Mathematics | Natural Sciences | Matematik | Mathematical Analysis | multiply-connected domains

Publication

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0065-9266, 09/2006, Volume 183, Issue 861, pp. 1 - 1

In this memoir, we prove that the universal Teichmuller space T(1) carries a new structure of a complex Hilbert manifold and show that the connected component...

DETERMINANTS | THEOREM | Universal Teichmuller space | Weil-Petersson metric | period mapping | RIEMANN SURFACES | Bers embedding | Bers coordinates | Riemann curvature tensor | STRING THEORY | Hilbert manifold structure | variation of the hyperbolic metric | Grunsky operators | Fredholm determinant | CIRCLE | MATHEMATICS | universal Liouville action | Kahler potential | OPERATORS | GEOMETRY

DETERMINANTS | THEOREM | Universal Teichmuller space | Weil-Petersson metric | period mapping | RIEMANN SURFACES | Bers embedding | Bers coordinates | Riemann curvature tensor | STRING THEORY | Hilbert manifold structure | variation of the hyperbolic metric | Grunsky operators | Fredholm determinant | CIRCLE | MATHEMATICS | universal Liouville action | Kahler potential | OPERATORS | GEOMETRY

Journal Article

15.
Full Text
Faber polynomials with applications to univalent functions with quasiconformal extensions

Science in China, Series A: Mathematics, ISSN 1006-9283, 10/2009, Volume 52, Issue 10, pp. 2121 - 2131

We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In...

Grunsky operator | Univalent function | Faber polynomial | Quasiconformal mapping | MATHEMATICS | quasiconformal mapping | univalent function

Grunsky operator | Univalent function | Faber polynomial | Quasiconformal mapping | MATHEMATICS | quasiconformal mapping | univalent function

Journal Article

Complex Variables, Theory and Application: An International Journal, ISSN 0278-1077, 08/1997, Volume 33, Issue 1-4, pp. 113 - 127

We investigate some coefficient properties of univalent functions related to their Grunsky operators and quasiconformal extendibility. We find some bounds of...

AMS No. 30C55 | Coefficient bounds | AMS No. 30C75 | Quasiconformally extendible univalent functions | The Grunsky operator | AMS No. 30C50

AMS No. 30C55 | Coefficient bounds | AMS No. 30C75 | Quasiconformally extendible univalent functions | The Grunsky operator | AMS No. 30C50

Journal Article

Complex Variables, Theory and Application: An International Journal, ISSN 0278-1077, 10/2000, Volume 42, Issue 4, pp. 289 - 307

This paper deals with the pull-back operator on the real-valued harmonic Dirichlet space by a quasisymmetric function. A new metric on Teichmüller spaces is...

Teichmüller space | harmonic function | Quasisymmetric function | Fredholm eigenvalue | Grunsky functional

Teichmüller space | harmonic function | Quasisymmetric function | Fredholm eigenvalue | Grunsky functional

Journal Article

Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2008, Volume 33, Issue 2, pp. 585 - 596

In recent work with Baranov, it was explained how to view the classical Grunsky inequalities in terms of an operator identity, involving a transferred Beurling...

Grunsky inequalities | Beurling transform | MATHEMATICS

Grunsky inequalities | Beurling transform | MATHEMATICS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2015, Volume 143, Issue 1, pp. 265 - 278

is demonstrated through the use of the Grunsky matrix.]]>

Grunsky matrix | Infinite Siegel disk | Conformal maps | Conformal welding | Quasi-symmetries | MATHEMATICS | MATHEMATICS, APPLIED | infinite Siegel disk | quasi-symmetries | conformal maps | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Grunsky matrix | Infinite Siegel disk | Conformal maps | Conformal welding | Quasi-symmetries | MATHEMATICS | MATHEMATICS, APPLIED | infinite Siegel disk | quasi-symmetries | conformal maps | Naturvetenskap | Mathematics | Natural Sciences | Matematik

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/1999, Volume 105, Issue 1-2, pp. 311 - 315

We show that the norm of the Grunsky operator generated by a univalent function does not decrease with a pth root transformation, p≥2. The result is sharp for...

30C45 | 30C70 | The Grunsky norm P th root transformation | 30C35 | Univalent functions

30C45 | 30C70 | The Grunsky norm P th root transformation | 30C35 | Univalent functions

Journal Article

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