We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*) x(t) + a(t)(Tx)(t) = b(t), where and are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial . By means of the Riemann boundary value problems, we give an algebraic method to obtain all solutions of equation (*) in closed form.
@article{bwmeta1.element.bwnjournal-article-apmv63z3p293bwm,
author = {Nguyen Van Mau and Nguyen Minh Tuan},
title = {On solutions of integral equations with analytic kernels and rotations},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {293-300},
zbl = {0854.47034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p293bwm}
}
Nguyen Van Mau; Nguyen Minh Tuan. On solutions of integral equations with analytic kernels and rotations. Annales Polonici Mathematici, Tome 63 (1996) pp. 293-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p293bwm/
[00000] [1] F. D. Gakhov, Boundary Value Problems, Oxford, 1966 (3rd Russian complemented and corrected edition, Moscow, 1977). | Zbl 0141.08001
[00001] [2] Nguyen Van Mau, Generalized algebraic elements and linear singular integral equations with transformed argument, Wydawnictwa Politechniki Warszawskiej, Warszawa, 1989.
[00002] [3] Nguyen Van Mau, Boundary value problems and controllability of linear systems with right invertible operators, Dissertationes Math. 316 (1992). | Zbl 0749.34034
[00003] [4] D. Przeworska-Rolewicz and S. Rolewicz, Equations in Linear Spaces, Monografie Mat. 47, PWN, Warszawa, 1968. | Zbl 0181.40501