One-Dimensional Linear Singular Integral Equations

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This monograph serves as the second volume of a graduate textbook on the modern theory of linear one-dimensional singular integral equations, which are increasingly significant due to their wide-ranging applications and the fact that they can often be solved explicitly. This volume builds upon material from the authors' earlier work published in 1973 and 1979, but it features numerous additions and complementary content that enhance its structure and accessibility for a broader audience. While the first volume focused on closed curves and continuous coefficients, this second volume addresses general curves and discontinuous coefficients. The text emphasizes key topics such as the invertibility and Fredholmness of singular integral operators, with a particular focus on inversion methods. The authors express gratitude to their editor, translator, and typist for their dedicated contributions to the project.