On the ill-posed character of the Lorentz integral transform

Details On the ill-posed character of the Lorentz integral transform On the ill-posed character of the Lorentz integral transform

2009-02-06

arxiv.org/abs/0902.1081v1

Physics

Nuclear Physics

Nuclear Theory

13 pages, 3 figures

Scientific paper

10.1007/s00601-009-0050-7

An exact inversion formula for the Lorentz integral transform (LIT) is provided together with the spectrum of the LIT kernel. The exponential increase of the inverse Fourier transform of the LIT kernel entering the inversion formula explains the ill-posed character of the LIT approach. Also the continuous spectrum of the LIT kernel, which approaches zero points necessarily to the same defect. A possible cure is discussed and numerically illustrated.

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