scholarly journals Rational Chebyshev approximation to certain entire functions of zero order on the positive real axis. II

1976 ◽  
Vol 54 (1) ◽  
pp. 251-251
Author(s):  
A. R. Reddy
Keyword(s):  
Real Axis ◽  
Entire Functions ◽  
Chebyshev Approximation ◽  
Zero Order ◽  
Positive Real Axis ◽  
Positive Real ◽  
Axis Ii ◽  
Rational Chebyshev ◽  
Rational Chebyshev Approximation

scholarly journals Möbius convolutions and the Riemann hypothesis

2005 ◽  
Vol 2005 (22) ◽  
pp. 3599-3608 ◽  
Author(s):  
Luis Báez-Duarte
Keyword(s):  
Real Axis ◽  
Riemann Hypothesis ◽  
Entire Functions ◽  
General Theorem ◽  
Positive Real Axis ◽  
Positive Real ◽  
Necessary And Sufficient Criteria ◽  
Necessary And Sufficient

The well-known necessary and sufficient criteria for the Riemann hypothesis of M. Riesz and of Hardy and Littlewood, based on the order of certain entire functions on the positive real axis, are here embedded in a general theorem for a class of entire functions, which in turn is seen to be a consequence of a rather transparent convolution criterion. Some properties of the convolutions involved sharpen what is hitherto known for the Riesz function.

scholarly journals An Extension of the Almost Isolated Singularity of Finite Exponential Order

1964 ◽  
Vol 14 (2) ◽  
pp. 137-141
Author(s):  
R. Wilson
Keyword(s):  
Real Axis ◽  
Taylor Series ◽  
Positive Real Axis ◽  
Isolated Singularity ◽  
Positive Real ◽  
Small Disk ◽  
Exponential Order ◽  
Disk Centre ◽  
Image Position

Let f(z) be represented on its circle of convergence |z| = 1 by the Taylor seriesand suppose that its sole singularity on |z| = 1 is an almost isolated singularity at z = 1. In the neighbourhood of such a singularity f(z) is regular on a sufficiently small disk, centre z = 1, with the outward drawn radius along the positive real axis excised. If also in this neighbourhood |f(z)| e−(1/δ)ρ remains bounded for some finite ρ, where δ is the distance from the excised radius, then the singularity is said to be of finite exponential order.

Dependence of Best Rational Chebyshev Approximations on the Domain

1977 ◽  
Vol 20 (4) ◽  
pp. 451-454 ◽  
Author(s):  
Charles B. Dunham
Keyword(s):  
Sufficient Conditions ◽  
Chebyshev Approximation ◽  
Error Norm ◽  
Rational Chebyshev ◽  
Rational Chebyshev Approximation

Sufficient conditions are given for the error norm and coefficients of best rational Chebyshev approximation on a domain to depend continuously on the domain. Examples of discontinuity are given.

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