What is it about?
We provide specific insights into how the average behavior of the Fourier transform changes over time for certain types of measures. These measures are continuous and may exhibit power-law patterns. This has practical applications in the field of quantum mechanics.
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Why is it important?
This is important because the Fourier transform of measures determines how quantum systems evolve over time. When dealing with continuous measures, one expect quantum transport. If these measures have power singularities, we offer precise predictions about their average asymptotic over time. It is worth mentioning that some quantum quantities do not capture such singularities.
Perspectives
Short time perspectives include other applications of the abstract results in important models, physical and mathematical. It would also be interesting to generalize the results to other types of singularities and include, somehow, sharp estimates to families of singular continuous measures.
Cesar Rogerio de Oliveira
Universidade Federal de Sao Carlos
Read the Original
This page is a summary of: On the Fourier asymptotics of absolutely continuous measures with power-law singularities, Journal of Mathematical Physics, January 2024, American Institute of Physics,
DOI: 10.1063/5.0149320.
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