Convolution-type integral operators in complex approximation

DOI10.1007/BF03321000zbMath1011.30031OpenAlexW2083173262MaRDI QIDQ1851474

Sorin Gheorghe Gal

Publication date: 29 May 2003

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321000

zbMATH Keywords

Cesàro meanstrigonometric polynomialsbest approximationmoduli of smoothnessFejér kernelcomplex approximationshape preserving propertiesconvolution-type operatorsJackson kernelglobal smoothness preservationde-la-Valée-Poussin meansJackson-type convolution operator

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Approximation in the complex plane (30E10) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Approximations and expansions (41A99)

Related Items (9)

Approximation by polynomials on quaternionic compact sets ⋮ De la Vallée Poussin means in Hardy spaces ⋮ Density of polyanalytic polynomials in complex and quaternionic polyanalytic weighted Bergman spaces ⋮ Density of complex and quaternionic polyanalytic polynomials in polyanalytic Fock spaces ⋮ Approximation by convolution polyanalytic operators in the complex and quaternionic compact unit balls ⋮ Polynomial approximation in quaternionic Bloch and Besov spaces ⋮ Quantitative approximations by convolution polynomials in Bergman spaces ⋮ Geometric and approximation properties of some singular integrals in the unit disk ⋮ Polynomial approximation in slice regular Fock spaces

Cites Work

• Remarks on de la Vallée Poussin means and convex conformal maps of the circle
• Geometric properties of the Cesàro means
• Mergelyan sets and the modulus of continuity of analytic functions
• Best approximation and saturation on domains bounded by curves of bounded rotation
• Close-to-convex schlicht functions
• On global smoothness preservation in complex approximation
• Degree of Approximation by Polynomials in the Complex Domain. (AM-9)
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