Free channel Fourier transform in the long-range \(N\)-body problem. (English) Zbl 0866.70008
Free channel generalized eigenfunctions are constructed using the Green’s function, similarly as in the two-body problem. The authors’ method allows to prove smoothness of the momenta as well as to describe the growth properties in configuration space of the generalized eigenfunctions. The authors actually span the free channel and identify the distorted Fourier transform. Finally, a class of long-range \(N\)-body operators with two-body potentials decaying faster than \(r^{-\varepsilon}\) for some \(\varepsilon > 0\) is considered.
Reviewer: B.D.Jovanović (Novi Sad)
MSC:
| 70F10 | \(n\)-body problems |
| 81V70 | Many-body theory; quantum Hall effect |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
generalized eigenfunctions; Green’s function; configuration space; distorted Fourier transform; two-body potentialsReferences:
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