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Matematicheskie Zametki, 2009, Volume 86, Issue 4, Pages 612–627
DOI: https://doi.org/10.4213/mzm4727 (Mi mzm4727) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Generalized Limits and Related Asymptotic Formulas

A. A. Sedaev

Voronezh State Academy of Building and Architecture
Full-text PDF (513 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm4727
Abstract: On the basis of the new version of Karamata's theorem, stated in terms of generalized limits, we succeed in weakening the conditions of validity of the Connes asymptotic formulas studied by many authors. Using this approach, we can apply the criterion of “measurability” due to Connes for passing from generalized limits to ordinary limits.
Keywords: generalized limit, Dixmier trace, operator ideal, Marcinkiewicz space, Cesàro operator, Karamata theorem, Lebesgue–Stieltjes integral, Hilbert space, dilation operator.
Received: 15.12.2007
Revised: 15.03.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 4, Pages 577–590
DOI: https://doi.org/10.1134/S000143460909034X
Bibliographic databases:
UDC: 517.51
Language: Russian
Citation: A. A. Sedaev, “Generalized Limits and Related Asymptotic Formulas”, Mat. Zametki, 86:4 (2009), 612–627; Math. Notes, 86:4 (2009), 577–590
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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