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On the half inverse spectral problem for an integro-differential operatorButerin, S.A.Sat, M.convolutionhalf inverse problemIntegro-differential operatorinverse spectral problemBoundary conditionsDifferential equationsMathematical operatorsProblem solvingConvolution integralsConvolution kernelDifferential operatorsDirichlet boundary conditionFinite intervalsIntegro differential operatorInverse spectral problemsKernel functionInverse problemsWe consider the Sturm–Liouville differential operator on a finite interval with Dirichlet boundary conditions perturbed with a convolution integral operator. The inverse problem is studied of recovering the convolution kernel from a half spectrum, provided that the kernel function on the first half of the interval as well as the Sturm–Liouville potential on the entire interval are known a priori. Besides the uniqueness of a solution of this half inverse problem, we also obtain necessary and sufficient conditions of its solvability. A constructive procedure for solving the inverse problem is also provided. © 2016 Informa UK Limited, trading as Taylor & Francis Group.Taylor and Francis Ltd.2017Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/14808https://doi.org/10.1080/17415977.2016.12671711741-5977enInverse Problems in Science and Engineeringinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/14808