Trace formulas for the modified Mathieu equation

2021/02/26 by Takhtajan, Leon A.
#FOS: Mathematics #Primary 47E05 #Secondary 34E05 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2103.00038

Abstract

For the radial and one-dimensional Schrödinger operator H with growing potential q(x) we outline a method of obtaining the trace identities - an asymptotic expansion of the Fredholm determinant det_F(H-λI) as λ→-∞. As an illustrating example, we consider Schrödinger operator with the potential q(x)=2\cosh 2x, associated with the modified Mathieu equation.

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