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The authors would like to thank Patrick Gerard for pointing out an inaccuracy in a previous version of this paper. T. A. was supported by FQRNT. D.J. was supported by NSERC, FQRNT and Dawson fellowship. F. M. was supported by grant MTM2010-16467 (MEC), and wishes to acknowledge the support of ICMAT through its visiting faculty program.
Analysis of institutional authors
Macia, FabricioAuthorUNIFORM ESTIMATES FOR THE SOLUTIONS OF THE SCHRODINGER EQUATION ON THE TORUS AND REGULARITY OF SEMICLASSICAL MEASURES
Publicated to:Mathematical Research Letters. 19 (3): 589-599 - 2012-01-01 19(3), DOI: 10.4310/MRL.2012.v19.n3.a7
Authors: Aissiou, Tayeb; Jakobson, Dmitry; Macia, Fabricio
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Abstract
We establish uniform bounds for the solutions e(it Delta)u of the Schrodinger equation on arithmetic flat tori, generalizing earlier results by J. Bourgain. We also study the regularity properties of weak-* limits of sequences of densities of the form vertical bar e(it Delta)u(n)vertical bar(2) corresponding to highly oscillating sequences of initial data (u(n)). We obtain improved regularity properties of those limits using previous results by N. Anantharaman and F. Macia on the structure of semiclassical measures for solutions to the Schrodinger equation on the torus.
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Quality index
Bibliometric impact. Analysis of the contribution and dissemination channel
The work has been published in the journal Mathematical Research Letters due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2012, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics (Miscellaneous).
From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 1.19, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jul 2025)
Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-07-27, the following number of citations:
- WoS: 7
- Scopus: 8
Impact and social visibility
Leadership analysis of institutional authors
This work has been carried out with international collaboration, specifically with researchers from: Canada.
There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (MACIA LANG, FABRICIO).