• Sergey V. Lototsky
  • Boris L. Rozovsky
Part of the Universitext book series (UTX)


We use the same notation x for a point in the real line \(\mathbb{R}\) or in a d-dimensional Euclidean space \(\mathbb{R}^{\mathrm{d}}\). For \(x = (x_{1},\ldots,x_{\mathrm{d}}) \in \mathbb{R}^{\mathrm{d}}\), \(\vert x\vert = \sqrt{x_{1 }^{2 } +\ldots +x_{\mathrm{d} }^{2}}\); for \(x,y \in \mathbb{R}^{\mathrm{d}}\), xy = x 1 y 1 + + x d y d. Integral over the real line can be written either as \(\int _{\mathbb{R}}\) or as + . Sometimes, when there is no danger of confusion, the domain of integration, in any number of dimensions, is omitted altogether.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sergey V. Lototsky
    • 1
  • Boris L. Rozovsky
    • 2
  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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