| Subject |
Integral equations and integral transforms |
| Title |
On the spectrum of Volterra integral equation with the "incompressible" kernel |
| Author(s) |
M.M. Amangaliyeva, M.T. Jenaliyev, M.T. Kosmakova, M.I. Ramazanov |
| Keywords |
singular Volterra integral equation, spectrum, "incompressible" kernel, eigenfunction, Abel equation |
| Abstract |
In the article the singular Volterra integral equation of the second kind is considered which has the "incompressible" kernel. It is shown that the corresponding homogeneous equation has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing parameter. The equation is reduced to Abel equation by the regularization method. The eigenfunctions of the equation are found in an explicit form. It is proved the solvability theorem of the inhomogeneous equation in a case when the right-hand side of the equation belongs to a certain class. |
