Trace formulas for the modified Mathieu equation

  • Leon A. Takhtajan

    SUNY at Stony Brook, USA; Euler International Mathematical Institute, St. Petersburg, Russian Federation
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Abstract

For the radial and one-dimensional Schrödinger operator with growing potential we outline a method of obtaining the trace identities – an asymptotic expansion of the Fredholm determinant as . As an illustrating example, we consider Schrödinger operator with the potential , associated with the modified Mathieu equation.