Conservative systems of integral convolution equations on the half-line and the entire line

Journal Article · Sun Jun 30 04:00:00 EDT 2002 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2002V193N06ABEH000660; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21205692

Engibaryan, N B ^[1]

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

The following system of integral convolution equations is considered: f(x)=g(x)+{integral}{sub a}{sup {infinity}}K(x-t)f(t)dt, -{infinity}{<=}a<{infinity}, where the (mxm)-matrix-valued function K satisfies the conditions of conservativeness K{sub ij} element of L{sub 1}(R), K{sub ij}{>=}0, A{identical_to}{integral}{sub -{infinity}}{sup {infinity}}K(x)dx element of P{sub N}, r(A)=1. Here P{sub N} is the class of non-negative indecomposable (mxm)-matrices and r(A) is the spectral radius of the matrix A. For a=0 the equation in question is a conservative system of Wiener-Hopf integral equations. For a=-{infinity} this is the multidimensional renewal equation on the entire line. Questions of the solubility of the inhomogeneous and the homogeneous equations, asymptotic and other properties of solutions are considered. The method of non-linear factorization equations is applied and developed in combination with new results in multidimensional renewal theory.

• OSTI ID: 21205692
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 6 Vol. 193; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
FACTORIZATION
FUNCTIONS
INTEGRAL EQUATIONS
INTEGRALS
MATRICES
NONLINEAR PROBLEMS