Noether Theorem of a Kind of Singular Integral Equation with Hilbert Kernel on Open Arcs

Singular Integral ◽

Noether Theorem ◽

Hilbert Kernel ◽

General Solutions ◽

Plemelj Formula ◽

Complex Functions

We discussed a kind of singular integral equation with Hilbert kernel on open arcs lying in a period strip. By using the method of complex functions, we obtained the extended Plemelj Formula with Hilbert kernel, and based on this, we obtained the general solutions and the solvable conditions for this kind of characteristic singular integral equation with Hilbert kernel on open arcs.

Noether Theorem of a Kind of Singular Integral Equation with Hilbert Kernel on Closed Contours

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.347-350.2596 ◽

2013 ◽

Vol 347-350 ◽

pp. 2596-2599

Author(s):

Li Xia Cao

Keyword(s):

Integral Equation ◽

General Solution ◽

Singular Integral ◽

Noether Theorem ◽

Hilbert Kernel ◽

Plemelj Formula ◽

Complex Functions

We considered a kind of singular integral equation with Hilbert kernel on closed contours. By using the method of complex functions, we obtain the extended Plemelj Formula with Hilbert kernel, and based on this, we obtained the related conditions of solvability and the general solution for the characteristic singular integral equation with Hilbert kernel on closed contours.

Proceedings of the 2nd International Conference On Systems Engineering and Modeling ◽

Noether theorem of a kind of singular integral equation with Hilbert kernel on open arcs

10.2991/icsem.2013.90 ◽

2013 ◽

Author(s):

Li-xia Cao

Keyword(s):

Integral Equation ◽

Singular Integral ◽

Noether Theorem ◽

Regularization Method for Complete Singular Integral Equation with Hilbert Kernel on Open Arcs

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.765-767.643 ◽

2013 ◽

Vol 765-767 ◽

pp. 643-646

Author(s):

Li Xia Cao

Keyword(s):

Integral Equation ◽

Integral Equations ◽

Singular Integral ◽

Regularization Method ◽

Singular Integral Equations ◽

Noether Theorem ◽

We considered the regularization method for a kind of complete singular integral equation with Hilbert kernel on open arcs lying in a period strip. And based on this, we obtained the solvable Noether theorem for this kind of complete singular integral equations.

Proceedings of the 2nd International Symposium on Computer, Communication, Control and Automation ◽

Noether theorem of a kind of singular integral equation with Hilbert kernel on closed contours

10.2991/isccca.2013.76 ◽

2013 ◽

Author(s):

Li-xia Cao

Keyword(s):

Integral Equation ◽

Singular Integral ◽

Noether Theorem ◽

The approximate solution of a non-linear characteristic singular integral equation with a hilbert kernel

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(69)90168-2 ◽

1969 ◽

Vol 9 (5) ◽

pp. 263-266

Author(s):

V.G. Ivanitskii

Keyword(s):

Integral Equation ◽

Approximate Solution ◽

Singular Integral ◽

Hilbert Kernel ◽

Linear Characteristic ◽

Non Linear

A singular integral equation with Hilbert kernel in a class of distributions

Differential Equations ◽

10.1134/s0012266106090084 ◽

2006 ◽

Vol 42 (9) ◽

pp. 1302-1311

Author(s):

A. V. Setukha

Keyword(s):

Integral Equation ◽

Singular Integral ◽

An approximate solution of a complete linear singular integral equation with the Hilbert kernel

Mathematical Notes ◽

10.1007/bf01159864 ◽

1987 ◽

Vol 41 (5) ◽

pp. 389-399

Author(s):

A. A. Babaev ◽

B. I. Musaev

Keyword(s):

Integral Equation ◽

Approximate Solution ◽

Singular Integral ◽

On the approximation by the method of averaging functional corrections of the solution of a characteristic singular integral equation with a Hilbert kernel

Ukrainian Mathematical Journal ◽

10.1007/bf01085202 ◽

1970 ◽

Vol 21 (6) ◽

pp. 699-704

Author(s):

V. G. Ivanitskii

Keyword(s):

Integral Equation ◽

Singular Integral ◽

Method Of Averaging ◽

Proceedings of the 2nd International Conference On Systems Engineering and Modeling ◽

Regularization method for complete singular integral equation with Hilbert kernel on open arcs

10.2991/icsem.2013.210 ◽

2013 ◽

Author(s):

Li-xia Cao

Keyword(s):

Integral Equation ◽

Singular Integral ◽

Regularization Method ◽

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2008-0010 ◽

2008 ◽

Vol 8 (2) ◽

pp. 143-154 ◽

Cited By ~ 1

Author(s):

P. KARCZMAREK

Keyword(s):

Integral Equation ◽

Approximate Solution ◽

Half Plane ◽

Singular Integral ◽

Trigonometric Polynomials ◽

Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.