scholarly journals Monotonicity of the error term in Gauss-Turán quadratures for analytic function

2007 ◽  
Vol 48 (4) ◽  
pp. 567-581 ◽  
Author(s):  
Gradimir V. Milovanović ◽  
Miodrag M. Spalević
Keyword(s):  
Analytic Function ◽  
Weight Function ◽  
Error Estimates ◽  
Complex Plane ◽  
Error Term ◽  
Quadrature Formulae

AbstractFor Gauss–Turán quadrature formulae with an even weight function on the interval [−1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than I, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some ℓ2-error estimates are considered.

On BMOA for Riemann Surfaces

1981 ◽  
Vol 33 (5) ◽  
pp. 1255-1260 ◽  
Author(s):  
Thomas A. Metzger
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Complex Plane ◽  
Riemann Surfaces ◽  
Hardy Class ◽  
Image Position

Let Δ denote the unit disk in the complex plane C. The space BMO has been extensively studied by many authors (see [3] for a good exposition of this topic). Recently, the subspace BMOA (Δ) has become a topic of interest. An analytic function f, in the Hardy class H2(A), belongs to BMOA (Δ) if(1)whereIt is known (see [3, p. 96]) that (1) is equivalent to(2)

Complex Approximation and Simultaneous Interpolation on Closed Sets

1977 ◽  
Vol 29 (4) ◽  
pp. 701-706 ◽  
Author(s):  
P. M. Gauthier ◽  
W. Hengartner
Keyword(s):  
Analytic Function ◽  
Complex Plane ◽  
Closed Subset ◽  
Finite Complex ◽  
Complex Approximation ◽  
Closed Sets ◽  
Limit Points ◽  
Simultaneous Interpolation ◽  
Complex Valued

Let ƒ be a complex-valued function denned on a closed subset F of the finite complex plane C, and let {Zn} be a sequence on F without limit points. We wish to find an analytic function g which simultaneously approximates ƒ uniformly on F and interpolates ƒ at the points {Zn}.

On the error term of the filon quadrature formulae

1987 ◽  
Vol 27 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Ulf Torsten Ehrenmark
Keyword(s):  
Error Term ◽  
Quadrature Formulae

scholarly journals Riemann-Stieltjes operators between Bergman-type spaces andα-Bloch spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Complex Plane ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Bloch Spaces ◽  
Type Spaces

We study the following integral operators:Jgf(z)=∫0zf(ξ)g′(ξ)dξ;Igf(z)=∫0zf′(ξ)g(ξ)dξ, wheregis an analytic function on the open unit disk in the complex plane. The boundedness and compactness ofJg,Igbetween the Bergman-type spaces and theα-Bloch spaces are investigated.

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