Degenerate multidimensional dispersion laws
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 20-33
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A study is made of the degeneracy of multidimensional dispersion laws $\omega ({\mathbf k})$, increasing infinitely at $|{\mathbf k}|\to \infty$ and satisfying a number of additional conditions is investigated. With the assumption of satisfying condition (4) by corresponding function of degeneracy $f(\mathbf {k})$ it is proved that only two-dimensional dispersion laws such as $\omega (p, q)=p^3\Omega (q/p)+cp\Omega _1(q/p)$ $\bigl (|p|, |q|\gg 1\bigr )$ can be generated relatively to the process $1\to 2$. Here $p\psi (q/p)=f(p, q)$ is the
corresponding unique function of degeneracy. Number of conditions were found
which should be satisfied by function $\Omega (\xi )$. An explicit form of the
degenerate dispersion law with the polynomial function $p^3\Omega (q/p)$ is
found.
@article{TMF_1993_95_1_a1,
author = {D. D. Tskhakaya},
title = {Degenerate multidimensional dispersion laws},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {20--33},
publisher = {mathdoc},
volume = {95},
number = {1},
year = {1993},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_1_a1/}
}
D. D. Tskhakaya. Degenerate multidimensional dispersion laws. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 20-33. http://geodesic.mathdoc.fr/item/TMF_1993_95_1_a1/