Setting and solving several factorization problems for integral operators

Journal Article · Sun Dec 31 04:00:00 EST 2000 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2000V191N12ABEH000529; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202988

Engibaryan, N B ^[1]

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1. Centre of Mathematical Physics Byurakan Astrophysical Observatory National Academy of Sciences of Armenia (Armenia)

The problem of factorization I-K=(I-U{sub -})(I-U{sub +}), is considered. Here I is the identity operator, K is a fixed integral operator of Fredholm type: (Kf)(x)={integral}{sub a}{sup b}k(x,t)f(t)dt, -{infinity}{<=}a<b{<=}+{infinity}, U{sub {+-}} are unknown upper and lower Volterra operators. Classes of generalized Volterra operators U{sub {+-}} are introduced such that I-U{sub {+-}} are not necessarily invertible operators in the spaces of functions on (a,b) under consideration. A combination of the method of non-linear factorization equations and a priori estimates brings forth new results on the existence and properties of the solution to this problem for k{>=}0, both in the subcritical case {mu}<1 and in the critical case {mu}=1, where {mu}=r(K) the spectral radius of the operator K. In addition, the problem of non-Volterra factorization is posed and studied, when the kernels of U{sub +} and U{sub -} vanish on some parts S{sub -} and S{sub +} of the domain S=(a,b){sup 2} such that S{sub +} union S{sub -}=S.

• OSTI ID: 21202988
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 12 Vol. 191; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS
FACTORIZATION
FUNCTIONS
INTEGRALS
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
NONLINEAR PROBLEMS