@article{NguyenVanMau1996,
abstract = {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 $T = M_\{n₁,k₁\} ... M_\{n_m,k_m\}$ and $M_\{n_j,k_j\}$ 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 $P_T(t) = t³ - t$. By means of the Riemann boundary value problems, we give an algebraic method to obtain all solutions of equation (*) in closed form.},
author = {Nguyen Van Mau, Nguyen Minh Tuan},
journal = {Annales Polonici Mathematici},
keywords = {integral operators; singular integral equations; algebraic operators; Riemann boundary value problems; integral equations on the unit circle; analytic continuation; Fredholm equation},
language = {eng},
number = {3},
pages = {293-300},
title = {On solutions of integral equations with analytic kernels and rotations},
url = {http://eudml.org/doc/262785},
volume = {63},
year = {1996},
}
TY - JOUR
AU - Nguyen Van Mau
AU - Nguyen Minh Tuan
TI - On solutions of integral equations with analytic kernels and rotations
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 3
SP - 293
EP - 300
AB - 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 $T = M_{n₁,k₁} ... M_{n_m,k_m}$ and $M_{n_j,k_j}$ 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 $P_T(t) = t³ - t$. By means of the Riemann boundary value problems, we give an algebraic method to obtain all solutions of equation (*) in closed form.
LA - eng
KW - integral operators; singular integral equations; algebraic operators; Riemann boundary value problems; integral equations on the unit circle; analytic continuation; Fredholm equation
UR - http://eudml.org/doc/262785
ER -
