Boundary triples for a family of degenerate elliptic operators of Keldysh type

We consider a one-parameter family of degenerately elliptic operators L γ on the closed disk D, of Keldysh (or Kimura) type, which appears in prior work [15] by the authors and Mishra, related to the geodesic X-ray transform.Depending on the value of a constant γ ∈ R in the sub-principal term, we prove that either the minimal operator is self-adjoint (case |γ| ≥ 1), or that one may construct appropriate trace maps and Sobolev scales (on D and S 1 = ∂D) on which to formulate mapping properties, Dirichlet-to-Neumann maps, and extend Green's identities (case |γ| < 1).The latter can be reinterpreted in terms of a boundary triple for the maximal operator, or a generalized boundary triple for a distinguished restriction of it.The latter concepts, object of interest in their own right, provide avenues to describe sufficient conditions for self-adjointness of extensions of L γ,min that are parameterized in terms of boundary relations, and we formulate some corollaries to that effect.