Randomized trial investigates solutions of singular integral equations using orthogonal polynomials, suggesting effective methods for mathematical analysis.
Classes of generalized functions representing continuous linear functionals on the closures of the linear spans of Jacobi polynomial systems are constructed. Inversion formulas for singular integral equations with a Cauchy kernel in classes of generalized functions are obtained.
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N. B. Pleshchinskii (2026) studied this question.
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