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The aim of the present paper is to consider the solvability and solutions of systems of dual integral equations involving Fourier transforms. The uniqueness and existence theorems are proved in appropriate Sobolev spaces. We shall consider the cases: the case A(ξ) ∈ Σ ~α +(R) and the case A(ξ) ∈ Σ ~α o (R). | SOLVABILITY OF SYSTEMS OF DUAL INTEGRAL EQUATIONS INVOLVING FOURIER TRANSFORMS Nguyen Thi Ngan1 , College of Education - TNU Summary. The aim of the present paper is to consider the solvability and solutions of systems of dual integral equations involving Fourier transforms. The uniqueness and existence theorems are proved ~ in appropriate Sobolev spaces. We shall consider the cases: the case A(ξ) ∈ Σα + (R) and the case α ~ A(ξ) ∈ Σo (R). Key words: Fourier transform, systems of dual integral equations, mixed boundary value problems. 1 Introduction Dual integral equations arise in many areas of mathematical physics, especially in connection with mixed boundary value problems. Different contact problems of theory of elasticity, problems on strained states near cracks, some problems of electrostatics and other topics are among them. The theory of dual equations recently became very developed and is the subject of numerous investigations. Formal analytical methods for finding solutions to dual equations have been studied by many authors (see [4, 9]), but much less attention has been paid to solvability question of these equations. The dual integral equation of Titchmarsh’s type was investigated in [12] by distributional approach and in [1] on Lebesgue spaces. The solvability of dual integral equations involving Fourier transforms and dual series expansions involving orthogonal expansions of generalized functions was considered in [5-7]. Note that, dual integral equations for convolutions can be also reduced to the equations involving Fourier transforms. Some classes of those equations on semi-axes of the real axis were investigated in [3]. To our knowledge, the solvability of the systems of dual equations has been little studied. The aim of the present work is to consider the existence and uniqueness problems for systems of dual integral equations involving Fourier transforms of generalized functions, which are a generalization of some systems of dual equations .
