Naslov
Characteristic scales of bounded L2 sequences

Autori
Erceg, Marko ; Lazar, Martin

Izvornik
Asymptotic analysis (0921-7134) 109 (2018), 3-4; 171-192

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
semiclassical measures, H-measures, oscillatory sequence, concentratory sequence, characteristic scale, Kolmogorov-Riesz compactness theorem

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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