On line integrals of rational functions of two complex variables
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- by E. Azoff, K. Clancey and I. Gohberg PDF
- Proc. Amer. Math. Soc. 86 (1982), 229-235 Request permission
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
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E. Azoff, K. Clancey and I. Gohberg, On the spectra of finite-dimensional perturbations of matrix multiplication operators, Manuscripta Math. 30 (1980), 351-360.
—, Singular points of families of Fredholm integral operators Proceedings of the Toeplitz Memorial Conference, Operator Theory: Advances and Applications, Birkhauser-Verlag, Basel, (to appear).
Additional Information
- © Copyright 1982 American Mathematical Society
- 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