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Complex ΨDOSS and systems of complex differential equations

  • Sabir Umarov
Chapter
  • 1.1k Downloads
Part of the Developments in Mathematics book series (DEVM, volume 41)

Abstract

In Chapters 4–7 we discussed pseudo-differential equations of integer and fractional orders with ψDOSS depending on real variables \(t \in \mathbb{R}\) and \(x \in \mathbb{R}^{n}\). In this section we will discuss differential and pseudo-differential equations depending on complex variables \(t =\tau +i\sigma \in \mathbb{C}\) and \(z = x + iy \in \mathbb{C}^{n}.\) Consider two simple examples with the one-dimensional “spatial” variable:
  1. (i)

    “complex wave” equation, and

     
  2. (ii)

    “complex heat” equation.

     

Keywords

Pseudo-differential Equations Meromorphic Symbols Cauchy-Kowalevsky Theorem General Boundary Value Problems Exponential Functionals 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sabir Umarov
    • 1
  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

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