Geodesic
Functional Cantor equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 355-361

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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.
Keywords: inverse scattering problem, Fourier–Stieltjes integral, $q$-difference equation. 
@article{TMF_2016_189_3_a2,
     author = {A. B. Shabat},
     title = {Functional {Cantor} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--361},
     publisher = {mathdoc},
     volume = {189},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a2/}
}
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A. B. Shabat. Functional Cantor equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 355-361. http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a2/