Аңдатпа
The article addresses the singular Volterra integral equation of the second kind, which has the ’incompressible’ kernel. It is shown that the corresponding homogeneous equation on |λ| ≥ exp{|arg λ|}, arg λ ∈ [−π,π] has a continuous spectrum, and the multiplicity of the characteristic numbers grows with increasing |λ|. We use the Carleman-Vekua regularization method. We introduce the characteristic integral equation. We prove that the initial integral equation has eigen-functions, the multiplicity of which depends on the value of the spectral parameter λ. We prove the solvability theorem of the nonhomogeneous equation in a case when the right-hand side of the equation belongs to a certain class.