Integration of virtually continuous functions over bistochastic measures and the trace formula for nuclear operators
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A. M. Vershik, P. B. Zatitskiĭ and F. V. Petrov
Translated by: F. Petrov - St. Petersburg Math. J. 27 (2016), 393-398
- DOI: https://doi.org/10.1090/spmj/1394
- Published electronically: March 30, 2016
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Abstract:
Birman’s definition of the integral trace of a nuclear operator as an integral over the diagonal is linked to the recent concept of virtually continuous measurable functions of several variables [2, 3]. Namely, it is shown that the construction of Birman is a special case of the general integration of virtually continuous functions over polymorphisms (or bistochastic measures), which in particular makes it possible to integrate such functions over some submanifolds of zero measure. Virtually continuous functions have similar application to embedding theorems (see [2]).References
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Bibliographic Information
- A. M. Vershik
- Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences; St. Petersburg State University; A. A. Kharkevich Institute for Information Transition Problems, Russian Academy of Sciences
- MR Author ID: 178105
- Email: vershik@pdmi.ras.ru
- P. B. Zatitskiĭ
- Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences; Chebyshev Laboratory at St. Petersburg State University
- MR Author ID: 895184
- Email: paxa239@yandex.ru
- F. V. Petrov
- Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences; St. Petersburg State University
- MR Author ID: 689029
- ORCID: 0000-0003-1693-2745
- Email: fedyapetrov@gmail.com
- Received by editor(s): September 5, 2014
- Published electronically: March 30, 2016
- Additional Notes: Supported by the RFBR grants 14-01-00373_A and 13-01-12422-OFI-m; President of Russia grant MK-6133.2013.1; Government of Russia grant 11.G34.31.0026 (Chebyshev Laboratory); JSC “GazpromNeft”; SPbSU grant, project 6.38.223.2014.
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 393-398
- MSC (2010): Primary 28A25
- DOI: https://doi.org/10.1090/spmj/1394
- MathSciNet review: 3570957
Dedicated: To Nina Nikolaevna Ural’tseva on the occasion of her anniversary