Geodesic
Fourier-Bessel functions of singular continuous measures and their many asymptotics
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 409-430
We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier-Bessel functions, in the argument, the order, and in certain combinations of the two is required to solve a number of problems arising in quantum mechanics. We discuss known results, new approaches and open conjectures, hoping to justify our belief that these investigations may involve interesting discoveries, well beyond the quantum mechanical applications.
Classification : 42C05, 33E20, 28A80, 30E15, 30E20
Keywords: singular measures, Fourier transform, orthogonal polynomials, almost periodic Jacobi matrices, Fourier-Bessel functions, quantum intermittency, Julia sets, iterated function systems, generalized dimensions, potential theory 
@article{ETNA_2006__25__a7,
     author = {Mantica,  Giorgio},
     title = {Fourier-Bessel functions of singular continuous measures and their many asymptotics},
     journal = {Electronic transactions on numerical analysis},
     pages = {409--430},
     year = {2006},
     volume = {25},
     zbl = {1160.42310},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a7/}
}
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%J Electronic transactions on numerical analysis
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Mantica,  Giorgio. Fourier-Bessel functions of singular continuous measures and their many asymptotics. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 409-430. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a7/