A Procedure For Obtaining the Zeros of Functions or their Derivatives by Lagrangean Interpolation

1960 ◽  
Vol 39 (1-4) ◽  
pp. 141-150
Author(s):  
Prescott D. Crout
Keyword(s):  
Zeros Of Functions

scholarly journals NORMALITY AND SHARED SETS

2009 ◽  
Vol 86 (3) ◽  
pp. 339-354 ◽  
Author(s):  
MINGLIANG FANG ◽  
LAWRENCE ZALCMAN
Keyword(s):  
Positive Integer ◽  
Meromorphic Functions ◽  
Complex Numbers ◽  
Finite Complex ◽  
Shared Sets ◽  
Zeros Of Functions

AbstractLet ℱ be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least k+1. Let a and b be distinct finite complex numbers, and let k be a positive integer. If, for each pair of functions f and g in ℱ, f(k) and g(k) share the set S={a,b}, then ℱ is normal in D. The condition that the zeros of functions in ℱ have multiplicity at least k+1 cannot be weakened.

On the distribution of zeros of functions from weighted Bergman spaces

2009 ◽  
Vol 86 (1-2) ◽  
pp. 93-106 ◽  
Author(s):  
E. A. Sevast’yanov ◽  
A. A. Dolgoborodov
Keyword(s):  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Distribution Of Zeros ◽  
Zeros Of Functions

scholarly journals Zeros of functions of a quaternion variable

1959 ◽  
Vol 62 ◽  
pp. 496-501
Author(s):  
L. Kuipers ◽  
P.A.J. Scheelbeek
Keyword(s):  
Zeros Of Functions

scholarly journals On the zeros of functions in Bergman spaces and in some other related classes of functions

2005 ◽  
Vol 309 (2) ◽  
pp. 534-543
Author(s):  
Daniel Girela ◽  
M. Auxiliadora Márquez ◽  
José Ángel Peláez
Keyword(s):  
Bergman Spaces ◽  
Zeros Of Functions

The phase problem in scattering phenomena: the zeros of entire functions and their significance

1978 ◽  
Vol 360 (1700) ◽  
pp. 25-45 ◽  
Keyword(s):  
Entire Functions ◽  
Signal To Noise Ratio ◽  
Phase Problem ◽  
Distribution Of Zeros ◽  
Real Zeros ◽  
Zeros Of Entire Functions ◽  
Functions Of Exponential Type ◽  
Zeros Of Functions ◽  
The Fourier Transform ◽  
Complex Zeros

The paper outlines an approach to the calculation of the phase from intensity data based on the properties of the distribution of zeros of functions of exponential type. This leads to a reinterpretation of such phenomena as Gibbs’ or speckle, which underlines their intrinsic unity. The phase problem is solved for functions which present complex zeros by apodization, i.e. by creating a sufficiently large zero-free area. The method is based on a compromise between signal to noise ratio and resolution and is meaningful provided the apodization required is not too severe. Real zeros, for which the phase problem is trivial, occur only for the special case of eigenfunctions of the Fourier transform

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