On a General Concept for Separation of Variables
Josef Hainzl · SIAM Journal on Mathematical Analysis · 1982
A new definition of (generalized) separability for a linear operator L of arbitrary order is given which, when specialized to the Helmholtz operator, includes ordinary separability in nonorthogonal and “heat type” coordinates. On the basis of this definition, a set of commuting operators is explicitly constructed and various relationships between eigenvalue problems for these operators and separated equations corresponding to $Lu = 0$ are derived. Moreover, a transformation of Bäcklund type for separable operators is obtained.