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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The finite part of singular integrals in several complex variables
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by Xiaoqin Wang PDF
Trans. Amer. Math. Soc. 337 (1993), 771-793 Request permission

Abstract:

A divergent integral can sometimes be handled by assigning to it as its value the finite part in the sense of Hadamard. This is done by expanding the integral over the complement of a symmetric neighborhood of a singularity in powers of the radius, and throwing away the negative powers. In this paper the finite part of a singular integral of Cauchy type is defined, and this is then used to describe the boundary behavior of derivatives of a Cauchy-type integral. The finite part of a singular integral of Bochner-Martinelli type is studied, and an extension of the Plemelj jump formulas is shown to hold.
References
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 337 (1993), 771-793
  • MSC: Primary 32A25
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1120777-0
  • MathSciNet review: 1120777