Domains on which analytic functions satisfy quadrature identities
From MaRDI portal
Publication:1229989
DOI10.1007/BF02786704zbMath0337.30029OpenAlexW2047959295WikidataQ29299759 ScholiaQ29299759MaRDI QIDQ1229989
Harold S. Shapiro, Dov Aharonov
Publication date: 1976
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02786704
Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) General theory of conformal mappings (30C35) Boundary value problems in the complex plane (30E25) Moment problems and interpolation problems in the complex plane (30E05)
Related Items
Multivalued analytic continuation of the Cauchy transform ⋮ Regularity of a free boundary at the infinity point ⋮ Restriction operators, balayage and doubly orthogonal systems of analytic functions ⋮ Subsolutions and supersolutions in a free boundary problem ⋮ Harold Seymour Shapiro 1928--2021; life in mathematics, in memoriam ⋮ Quadrature domains and kernel function zipping ⋮ The Cauchy integral formula, quadrature domains, and Riemann mapping theorems ⋮ Combination Theorems in Groups, Geometry and Dynamics ⋮ A Moment Problem on Jordan Domains ⋮ On the Exponential Transform of Lemniscates ⋮ Subnormal operators and quadrature domains ⋮ On the relationship between Nevanlinna and quadrature domains ⋮ Real algebraic geometry of real algebraic Jordan curves in the plane and the Bergman kernel ⋮ Newtonian potential theory for unbounded sources and applications to free boundary problems ⋮ Application of half-order differentials on Riemann surfaces to quadrature identities for arc-length ⋮ Optimization and estimates of harmonic measure ⋮ Quadrature domains for the Bergman space in several complex variables ⋮ Singular and special points on quadrature domains from an algebraic geometric point of view ⋮ Analytic continuation of the exponential transform from convex cavities ⋮ Linear analysis of quadrature domains ⋮ An improved Riemann mapping theorem and complexity in potential theory ⋮ Line bundles defined by the Schwarz function ⋮ The adjoint of a composition operator via its action on the Szegő kernel ⋮ The isoperimetric inequality via approximation theory and free boundary problems ⋮ A vector equilibrium problem for symmetrically located point charges on a sphere ⋮ The Dirichlet and Neumann and Dirichlet-to-Neumann problems in quadrature, double quadrature, and non-quadrature domains ⋮ An answer to a question of A.\,Lubin: the lifting problem for commuting subnormals ⋮ The Bergman analytic content of planar domains ⋮ Asymptotic properties of unbounded quadrature domains the plane ⋮ A commutator formula for subnormal tuples of operators ⋮ Identification of nodal points of an elastic inclusion in elastic plane ⋮ Dynamics of Schwarz Reflections: The Mating Phenomena ⋮ Point source equilibrium problems with connections to weighted quadrature domains ⋮ The forbidden region for random zeros: Appearance of quadrature domains ⋮ Quadrature for quadrics ⋮ Scaling limits for internal aggregation models with multiple sources ⋮ The Mother Body Phase Transition in the Normal Matrix Model ⋮ Non-algebraic quadrature domains ⋮ Laplacian growth, sandpiles, and scaling limits ⋮ Szegő coordinates, quadrature domains, and double quadrature domains ⋮ On extreme Bloch functions with prescribed critical points ⋮ Null quadrature domains ⋮ Properties of mono-weakly hyponormal 2-variable weighted shifts ⋮ New conditions for uniform approximation by polyanalytic polynomials ⋮ Potato Kugel ⋮ On quadrature domains and an inverse problem in potential theory ⋮ Unnamed Item ⋮ On the uniqueness problem for quadrature domains ⋮ Uniformizing the boundaries of multiply connected quadrature domains using Fuchsian groups ⋮ Selected topics on quadrature domains ⋮ Hele-Shaw type flows in Rn ⋮ On the uniqueness theorem of Holmgren ⋮ Quadrature domains and the real quadratic family ⋮ Logarithmic equilibrium on the sphere in the presence of multiple point charges ⋮ Notes on the boundaries of quadrature domains ⋮ Minimal area problems for functions with integral representation ⋮ On the construction of multiply connected arc integral quadrature domains ⋮ Quadrature identities and the Schottky double ⋮ A minimal area problem in conformal mapping. II ⋮ Real separated algebraic curves, quadrature domains, Ahlfors type functions and operator theory ⋮ The Hele-Shaw flow and moduli of holomorphic discs ⋮ Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell ⋮ Topology of quadrature domains ⋮ Schwarz reflections and anti-holomorphic correspondences ⋮ A 1-point poly-quadrature domain of order 1 not biholomorphic to a complete circular domain ⋮ The resultant on compact Riemann surfaces ⋮ Superresolution of principal semi-algebraic sets ⋮ Uniqueness of Hahn-Banach extensions from certain spaces of analytic functions ⋮ A note on the critical points of the localization landscape ⋮ Density of quadrature domains in one and several complex variables ⋮ Xia's analytic model of a subnormal operator and its applications ⋮ A minimal area problem in conformal mapping ⋮ Ruminations on Hejhal's theorem about the Bergman and Szegő kernels ⋮ How to count zeroes of polynomials on quadrature domains using the Bezout matrix ⋮ On the exponential transform of multi-sheeted algebraic domains ⋮ Symmetry and Uniform Approximation by Analytic Functions ⋮ On a class of operators with finite rank self-commutators ⋮ Finite term relations for the exponential orthogonal polynomials ⋮ Traces of Commutators of Integral Operators – the Aftermath ⋮ Integrable structure of the Dirichlet boundary problem in multiply-connected domains ⋮ Subnormal operators, self-commutators, and pseudocontinuations ⋮ Quadrature domains in \({{\mathbb C}}^n\) ⋮ Linear analysis of quadrature domains. II ⋮ Exponential Transforms, Resultants and Moments ⋮ An Example of a Doubly Connected Domain which Admits a Quadrature Identity ⋮ Complexity in complex analysis. ⋮ Bers slices in families of univalent maps ⋮ On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the mean-value property of harmonic functions
- Bounded analytic functions
- The span of multiply connected domains
- On the Analytic Continuation of Mapping Functions
- Shorter Notes: On the Mean-Value Property of Harmonic Functions
- Weighted Mean Approximation in Carathéodory Regions.
- On the Mean-Value Property of Harmonic Functions
- Approximation in the Mean by Analytic Functions
- On the Mean-Value Property of Harmonic Functions