Reconstruction of a Pair Integral Operator of the Convolution Type
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For an arbitrary operator, we pose a general reconstruction problem inverse to the problem of finding solutions. For the pair operator considered, this problem is reduced to the equivalent problem of reconstruction of the kernels of the pair integral equation of the convolution type that generates this operator. In the cases investigated, we prove theorems that characterize the reconstruction of the corresponding kernels, which are constructed in terms of two functions from different Banach algebras of the type L1(−∞, ∞) with weight.
KeywordsIntegral Equation Integral Operator Banach Algebra Reconstruction Problem Equivalent Problem
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