Stokes matrices of a reducible double confluent Heun equation via monodromy matrices of a reducible general Heun equation with symmetric finite singularities
In this paper, the author studies the relation between the analytic invariants of the double confluent Heun operator (DCHO) and general Heun operator (GHO). The case is considered when the linear operator \(L\in\)DCHO is reducible. That is, \(L=L_{1}\circ L_{2}\) and there are depending on a small complex parameter \(\varepsilon\) linear operators \(L_{1\varepsilon}\), \(L_{2\varepsilon}\) such that \(\lim\limits _{\varepsilon\rightarrow0}L_{\mathrm{i\varepsilon}}=L_{i}(i=1,2)\) and \(L_{\varepsilon}=L_{1\varepsilon}\circ L_{2\varepsilon}\in\) GHO. Then, as the author shows, the analytical invariants of the \(L\) can be obtained from the analytical invariants of the \(L_{\varepsilon}\) by a limit transition on \(\varepsilon\). This is particularly true for the Stokes matrices.
reducible general Heun and double confluent Heun equations
scientific article; zbMATH DE number 7462072
scientific article