Functional Analysis and Its Applications

, Volume 50, Issue 3, pp 176–192 | Cite as

Automorphisms of the solution spaces of special double-confluent Heun equations



Two new linear operators determining automorphisms of the solution space of a special double-confluent Heun equation in the general case are obtained. This equation has two singular points, both of which are irregular. The obtained result is applied to solve the nonlinear equation of the resistively shunted junction model for an overdamped Josephson junction in superconductors. The new operators are explicitly expressed in terms of structural polynomials, for which recursive computational algorithms are constructed. Two functional equations for the solutions of the special double-confluent Heun equation are found.


special functions double-confluent Heun equation solution space automorphisms functional equations 


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  2. 2.All-Russia Research Institute of Physical-Technical and Radiotechnical Measurements (VNIIFTRI)Mendeleevo, Moscow oblastRussia

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