Functional Cantor equation
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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.
Keywordsinverse scattering problem Fourier–Stieltjes integral q-difference equation
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