Premium
Translation representation for automorphic solutions of the wave equation in non‐euclidean spaces, IV
Author(s) -
Lax Peter D.,
Phillips Ralph S.
Publication year - 1992
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160450203
Subject(s) - mathematics , automorphic form , completeness (order theory) , section (typography) , translation (biology) , euclidean geometry , pure mathematics , representation (politics) , wave equation , rank (graph theory) , mathematical analysis , combinatorics , geometry , biochemistry , chemistry , politics , messenger rna , advertising , political science , law , business , gene
In Part I of this series of papers we have defined the incoming and outgoing translation representations for automorphic solutions of the hyperbolic wave equations; in Part II we have proved the completeness of these representations when the fundamental polyhedron F has a finite number of sides with a finite or infinite volume, but is not compact. In Part IV we present a proof of completeness which is simpler than our original proof contained in Section 7 of Part II for the case when F has cusps of less than maximal rank; and we supply a proof for the case, not covered in Section 7, when the parabolic subgroup associated with such cusps contains twists.