Complex ΨDOSS and systems of complex differential equations

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


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.



Pseudo-differential Equations Meromorphic Symbols Cauchy-Kowalevsky Theorem General Boundary Value Problems Exponential Functionals 
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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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