IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-64999-8_7.html
   My bibliography  Save this book chapter

Global Cauchy Theorem

In: Complex Analysis and Dynamics in One Variable with Applications

Author

Listed:
  • Luis T. Magalhães

    (University of Lisbon, Instituto Superior Técnico)

Abstract

Chains, cycles and homology, global Cauchy theorem and formula, path homotopy and integral invariance, simply and multiply connected regions, homology basis, extensions of the maximum modulus principle including the Phragmén–Lindelöf Principle, Hardy Uncertainty Principle, order and type of entire functions, Denjoy–Carleman–Ahlfors theorem on the number of asymptotic values of entire functions. Exercises, including on Laplace transform and its application to solve differential equations, interpolation theorem for entire functions known as Sampling Theorem in telecommunications and related to the Nyquist sampling frequency, the Hadamard 3 circles theorem, and with applications to linear systems analysis and control, including the notions of transfer function, impulse response, Bode diagram, and linear feedback control systems.

Suggested Citation

  • Luis T. Magalhães, 2025. "Global Cauchy Theorem," Springer Books, in: Complex Analysis and Dynamics in One Variable with Applications, chapter 0, pages 115-141, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-64999-8_7
    DOI: 10.1007/978-3-031-64999-8_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-64999-8_7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.