Picard operators

Academic Article

Abstract

  • A linear differential expression Ly = y(n) + qn-2y(n-2) + ⋯ + q0y is called a Picard expression if its coefficients are elliptic functions (with common fundamental periods) and if the general solution of Ly = Ey is an everywhere meromorphic function (with respect to the independent variable) for all E ∈ ℂ. If L is a Picard expression we show that the differential equation Ly = Ey has n linearly independent Floquet solutions except when E is any of a finite number of exceptional values. Also the conditional stability set of a Picard expression (and hence the spectrum of the associated operator in L2 (ℝ)) consists of finitely many regular analytic arcs.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Weikard R
  • Start Page

  • 251
  • End Page

  • 266
  • Volume

  • 195