Approximation by polynomials and analytic functions in the areal mean

1968 ◽  
pp. 91-124 ◽  
Author(s):  
S. O. Sinanjan
Keyword(s):  
Analytic Functions ◽  
Approximation By Polynomials

scholarly journals Pointwise bounded approximation by polynomials

1992 ◽  
Vol 112 (1) ◽  
pp. 147-155 ◽  
Author(s):  
Anthony G. O'Farrell ◽  
Fernando Perez-Gonzalez
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Bounded Analytic Functions ◽  
Unbounded Component ◽  
Open Set ◽  
Approximation By Polynomials ◽  
Polynomial Hull ◽  
Image Position

For a bounded open set U ⊂ ℂ, we denote by H∞(U) the collection of all bounded analytic functions on U. We let X denote bdy (U), the boundary of U, Y denote the polynomial hull of U (the complement of the unbounded component of ℂ / X), and U* denote mt (Y), the interior of Y. We denote the sup norm of a function f: A → ℂ by ∥f∥A:We denote the space of all analytic polynomials by ℂ[z], and we denote the open unit disc by D and the unit circle by S1.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions

ON MONOTONIC AND ANALYTIC FUNCTIONS IN C ∞

1997 ◽  
Vol 23 (2) ◽  
pp. 697
Author(s):  
Cater
Keyword(s):  
Analytic Functions
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