Characteristic scales of bounded L2 sequences (CROSBI ID 250886)
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Erceg, Marko ; Lazar, Martin
engleski
Characteristic scales of bounded L2 sequences
Practical applications of semiclassical measures are tightly connected with a so called oscillatory property, prevailing leakage of information related to high frequencies. In this paper we propose a complementary, concentratory property which prevents loss of information related to low frequencies. We demonstrate that semiclassical measures attain the best performance level if both the properties are satisfied simultaneously, and address a question if this is possible to achieve for an arbitrary bounded L 2 sequence, providing a negative answer. Comparison of H- measures with semiclassical ones is presented, showing precedence of the latter for problems exhibiting just a single frequency scale. Finally, we present some (strong) compactness results based on the above properties.
semiclassical measures, H-measures, oscillatory sequence, concentratory sequence, characteristic scale, Kolmogorov-Riesz compactness theorem
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