Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis

1999 ◽  
Vol 18 (2) ◽  
pp. 379-391 ◽  
Author(s):  
S. Bernstein
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Hilbert Transform ◽  
Clifford Analysis ◽  
Singular Integral Equations ◽  
The Hilbert Transform

scholarly journals ON SOLUTION OF AMPLITUDE-PHASE PROBLEM

2018 ◽  
pp. 64-68 ◽  
Author(s):  
I. V. Boykov ◽  
Ya V. Zelina
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integrals ◽  
Singular Integral Equations ◽  
Quadrature Formulas ◽  
Two Dimensional ◽  
Phase Problem ◽  
The Fourier Transform ◽  
The Hilbert Transform ◽  
Unconventional Method

The paper describes an unconventional method of solving the amplitude-phase problem. The main properties of the Hilbert transform in the discrete and continual cases for one-dimensional and two-dimensional mappings are considered. These transformations are widely used to solve amplitude-phase problem. A numerical method for solving of two-dimensional amplitudephase problem is proposed. Preliminary information about the zeros of the Fourier transform of the initial signal is not required for this method. The method is based on the apparatus of nonlinear singular integral equations. Computational schemes for solving the corresponding nonlinear singular integral equations are developed. An algorithm for finding initial values for realization of iterative methods is proposed. Quadrature formulas of the calculation of singular integrals are proposed.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna

Singular integral equations in the bound-state problem

1965 ◽  
Vol 35 (3) ◽  
pp. 913-932 ◽  
Author(s):  
G. Cosenza ◽  
L. Sertorio ◽  
M. Toller
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Bound State ◽  
State Problem ◽  
Bound State Problem
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