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Erdélyi-Kober Fractional Integrals in the Real Matrix-Variante Case

  • A. M. Mathai
  • H. J. Haubold
Chapter
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 31)

Abstract

General notations on matrices, determinants, traces etc. are given in the introduction to Chap.  2 and hence they will not be repeated here. Before starting the discussion, we will need some Jacobians of matrix transformations here. For results on Jacobians, see Mathai [3]. For the real matrix-variate case, the determinant of X will be denoted by either det(X) or by |X|. When complex matrices are involved we will use the notation det(X) for determinant because we would like to reserve the notation |(⋅)| for the absolute value of (⋅). In this case the absolute value of the determinant of \(\tilde {X}\) will be written as \(|\mathrm {det}(\tilde {X})|\), denoting a matrix X in the complex domain as \(\tilde {X}\). All matrices appearing in this chapter are p × p real positive definite unless stated otherwise. Some Jacobians of matrix transformations will be stated here as lemmas without proofs. For proofs and other details, see Mathai [3].

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Copyright information

© The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • A. M. Mathai
    • 1
  • H. J. Haubold
    • 2
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  2. 2.Office for Outer Space Affairs United NationsViennaAustria

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