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Functional Cantor equation. (English. Russian original) Zbl 1358.81155
Theor. Math. Phys. 189, No. 3, 1712-1717 (2016); translation from Teor. Mat. Fiz. 189, No. 3, 355-361 (2016).
Summary: We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy \(q\)-difference functional equations. We study their asymptotic behavior and the distribution of zeros.

MSC:
81U40 Inverse scattering problems in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
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