Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T15:19:25.659Z Has data issue: false hasContentIssue false
  • English
  • Français

A VARIANT OF CAUCHY’S ARGUMENT PRINCIPLE FOR ANALYTIC FUNCTIONS WHICH APPLIES TO CURVES CONTAINING ZEROS

Part of: Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  18 January 2021

MAHER BOUDABRA Open the ORCID record for MAHER BOUDABRA [Opens in a new window]  and
GREG MARKOWSKY Open the ORCID record for GREG MARKOWSKY [Opens in a new window]
MAHER BOUDABRA*
Affiliation:
School of Mathematics, Monash University, Clayton, Victoria3800, Australia
GREG MARKOWSKY
Affiliation:
School of Mathematics, Monash University, Clayton, Victoria3800, Australia e-mail: [email protected]
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The standard version of Cauchy’s argument principle, applied to a holomorphic function f, requires that f has no zeros on the curve of integration. In this note, we give a generalisation of such a principle which covers the case when f has zeros on the curve, as well as an application.

Keywords

Cauchy’s argument principlewinding number

MSC classification

Primary: 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 103 , Issue 3 , June 2021 , pp. 486 - 492
Check for updates
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berenstein, C. and Gay, R., Complex Variables: An Introduction, Graduate Texts in Mathematics, 125 (Springer, New York, NY, 2012).Google Scholar
King, F., Hilbert Transforms (Cambridge University Press, Cambridge, 2009).Google Scholar
Remmert, R., Theory of Complex Functions, Readings in Mathematics, 122 (Springer, New York, NY, 2012).Google Scholar
Rudin, W., Real and Complex Analysis, 3rd edn (McGraw-Hill Education, New York, NY, 2001).Google Scholar
Spiegel, M. R., Complex Variables, Schaum’s Outline Series (McGraw-Hill, New York, NY, 2009).Google Scholar
Wyld, H. and Powell, G., Mathematical Methods for Physics (CRC Press, Baton Rouge, FL, 2020).CrossRefGoogle Scholar