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Cauchy-Hadamard integral with applications. (English) Zbl 1421.30052

Summary: The Cauchy type integral over curve \(\Gamma \) is traditional tool for solving of boundary-value problems of complex analysis. But it can diverge if length of the curve is infinite. We use Hadamard’s concept of finite part of integral for investigation of that situation.

MSC:

30E25 Boundary value problems in the complex plane
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References:

[1] Gakhov, F.D.: Boundary Value Problems. Nauka, Moscow (1977) · Zbl 0449.30030
[2] Muskhelishvili, N.I.: Singular Integral Equations. Nauka, Moscow (1962) · Zbl 0103.07502
[3] Jian-Ke, L.: Boundary Value Problems for Analytic Functions. World Scientific, Singapore (1993) · Zbl 0818.30027
[4] Hadamard, J.S.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale University Press, Oxford University Press, New Haven, Oxford (1923). (Reprint Dover 2003) · JFM 49.0725.04
[5] Rudin, W.: Real and Complex Analysis. McGraw-Hill, New York (1987) · Zbl 0925.00005
[6] Abreu-Blaya, R., Bory-Reyes, J., Kats, Boris A.: Integration over non-rectifiable curves and Riemann boundary value problems. J. Math. Anal. Appl. 380(1), 177-187 (2011) · Zbl 1218.30104 · doi:10.1016/j.jmaa.2011.02.068
[7] Kats, B.A., Katz, D.B.: Marcinkiewicz exponents and integrals over non-rectifiable paths. Math. Methods Appl. Sci. 39(12), 3402-3410 (2016) · Zbl 1350.30061 · doi:10.1002/mma.3787
[8] Katz, D.B., Kats B.A.: Interactions of germs with applications. Math. Methods. Appl. Sci. https://doi.org/10.1002/mma.4362 · Zbl 1373.30045
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