Analytic extrapolation in \(L^{\infty}\)-norm: An alternative approach to “QCD sum rules”. (English) Zbl 0664.46075
In view of physical applications (especially to “QCD Sum Rules”), the following problem, pertaining to analytic extrapolation techniques, is studied. We are considering “amplitudes”, which are (real) analytic functions in the complex plane cut along \(\Gamma =[s_ 0,\infty)\). A model \(F_ 0(s)\) of the amplitude is given through the values of \(F_ 0(s)\) on some interval \(\gamma =[s_ 2,s_ 1]\) (with \(s_ 1<s_ 0)\) and the values of its discontinuity on \(\Gamma\). These values are approximate, and are supplemented by prescribed error channels, measured in \(L^{\infty}\)-norm (both on \(\Gamma\) and \(\gamma)\). Investigating the compatibility between these data leads to an extremum problem which is solved up to a point where numerical methods can be implemented.
MSC:
| 46N99 | Miscellaneous applications of functional analysis |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 81V25 | Other elementary particle theory in quantum theory |
| 41A05 | Interpolation in approximation theory |
| 49J27 | Existence theories for problems in abstract spaces |
References:
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