- Tytuł:
- On solutions of integral equations with analytic kernels and rotations
- Autorzy:
-
Nguyen, Mau
Nguyen, Tuan - Tematy:
-
integral operators
singular integral equations
algebraic operators
Riemann boundary value problems - Pokaż więcej
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Powiązania:
- https://bibliotekanauki.pl/articles/1311183.pdf Link otwiera się w nowym oknie
- Opis:
- 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.
- Dostawca treści:
- Biblioteka Nauki
Artykuł