Extremal L_p-norms of linear operators and self-similar functionsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:We prove that for any p∈[1,+∞] a finite irreducible family of linear operators possesses an extremal norm corresponding to the p-radius of these operators. As a corollary, we derive a criterion for the L_p-contractibility property of linear operators and estimate the asymptotic growth of orbits for any point. These results are applied to the study of functional difference equations with linear contractions of the argument (self-similarity equations). We obtain a sharp criterion for the existence and uniqueness of solutions in various functional spaces, compute the exponents of regularity, and estimate moduli of continuity. This, in particular, gives a geometric interpretation of the p-radius in terms of spectral radii of certain operators in the space L_p[0,1].