ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 45, 46, 60 Yengibarian Noarair B., Byurakan Astrophys. Observatory, Armenia Nonlinear Factorization Equations of Integral Operators Let I be the unit operator and K - the Fredholm-type Integral operator on finite or infinite interval. Consider the factorization

I − K = (I − V −)(I − V +)

where V ± are a Volterrian operator to be defined. This problem is equivalent to some Nonlinear Factorization Equation (NFE) with respect to kernels of V ±. By studying the NFE some new Factorization theorems are proved, including a cases of non-invertible operator I − K. The results have been applied to homogeneous and including Wiener Hopf Eq., Renewal Eq. etc.