A Residue Calculus for Root Systems

  title={A Residue Calculus for Root Systems},
  author={E. P. VAN DEN BAN and H. SCHLICHTKRULL},
  • Published 1998
Let V be a ¢nite-dimensional real vector space on which a root system S is given. Consider a meromorphic function j on VC ˆ V ‡ iV , the singular locus of which is a locally ¢niteunion ofhyperplanes of the form fl 2 VC j hl; ai ˆ sg, a 2 S, s 2 R. Assumej is of suitable decay in the imaginarydirections, so that integrals ofthe form R Z‡iV j…l† dlmake sense forgeneric Z 2 V . A residue calculus is developed that allows shifting Z.This residue calculus can be used to obtain Plancherel and Paley… CONTINUE READING

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