Polynomial approximation of an entire function and generalized orders

DOI10.1016/0021-9045(77)90095-8zbMath0311.30034OpenAlexW1981974236MaRDI QIDQ1219384

S. M. Shah

Publication date: 1977

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(77)90095-8

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Approximation by polynomials (41A10) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (18)

Polynomial approximation of an entire function and rate of growth of Taylor coefficients ⋮ Approximation of entire transcendental functions of several complex variables in some Banach spaces for slow growth ⋮ Generalized growth orders for polymonogenic functions and related inequalities ⋮ Basics on growth orders of polymonogenic functions ⋮ The degree of convergence of entire functions and generalized type ⋮ On the best polynomial approximations of entire transcendental functions of many complex variables in some Banach spaces ⋮ The degree of polynomial approximation and interpolation of analytic functions ⋮ The generalized lower order of Dirichlet series ⋮ On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation ⋮ Entire monogenic functions of given proximate order and continuous homomorphisms ⋮ Polynomial approximation of an entire function of slow growth ⋮ Best polynomial approximation to certain entire functions ⋮ On the generalized order and generalized type of entire monogenic functions ⋮ The best polynomial approximations of entire transcendental functions with generalized growth order in Banach spaces \(\mathcal{E}_p^\prime (G)\) and \(\mathcal{E}_p(G)\), \(p \geqslant 1\) ⋮ Generalized growth and best approximation of entire functions in \(L^p\) -norm in several complex variables ⋮ On generalized growth of analytic functions solutions of linear homogeneous partial differential equation of second order ⋮ On the relation between maximum modulus, maximum term, and Taylor coefficients of an entire function ⋮ Approximation of entire functions over Carathéodory domains

Cites Work

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• On an extension of a result of S. N. Bernstein
• Über das Wachstum zusammengesetzter Funktionen
• On the rate of growth of entire functions of fast growth
• The Lower Order of Integral Functions
• On the lower order of integral functions
• Approximation of an entire function
• Approximation of an entire function
• Best polynomial approximation to certain entire functions

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