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On line integrals of rational functions of two complex variables


Authors: E. Azoff, K. Clancey and I. Gohberg
Journal: Proc. Amer. Math. Soc. 86 (1982), 229-235
MSC: Primary 32A20; Secondary 30C15, 45B05
DOI: https://doi.org/10.1090/S0002-9939-1982-0667280-8
MathSciNet review: 667280
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Abstract: Let $ \gamma $ be a simple rectifiable arc in the complex plane and $ r(z,w)$ a rational function of two complex variables. Set $ {r_\gamma }(z) = \int_\gamma {r(z,w)\;dw} $. The natural domain of $ {r_\gamma }$ has countably many components, and $ {r_\gamma }$ may vanish identically on infinitely many of these. It is shown however that unless $ \gamma $ spirals in to one of its endpoints, only finitely many zeros of $ {r_\gamma }$ are isolated.


References [Enhancements On Off] (What's this?)

  • [1] E. Azoff, K. Clancey and I. Gohberg, On the spectra of finite-dimensional perturbations of matrix multiplication operators, Manuscripta Math. 30 (1980), 351-360.
  • [2] -, Singular points of families of Fredholm integral operators Proceedings of the Toeplitz Memorial Conference, Operator Theory: Advances and Applications, Birkhauser-Verlag, Basel, (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0667280-8
Keywords: Zero set, line integral, rational function, spiral
Article copyright: © Copyright 1982 American Mathematical Society

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