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Integration of virtually continuous functions over bistochastic measures and the trace formula for nuclear operators. / Vershik, A. M.; Zatitskiĭ, P. B.; Petrov, F. V.
в: St. Petersburg Mathematical Journal, Том 27, № 3, 01.01.2016, стр. 393-398.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Integration of virtually continuous functions over bistochastic measures and the trace formula for nuclear operators
AU - Vershik, A. M.
AU - Zatitskiĭ, P. B.
AU - Petrov, F. V.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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]).
AB - 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]).
KW - Duality
KW - Quasibistochastic measures
KW - Virtally continuous function
UR - http://www.scopus.com/inward/record.url?scp=84963612586&partnerID=8YFLogxK
U2 - 10.1090/spmj/1394
DO - 10.1090/spmj/1394
M3 - Article
AN - SCOPUS:84963612586
VL - 27
SP - 393
EP - 398
JO - St. Petersburg Mathematical Journal
JF - St. Petersburg Mathematical Journal
SN - 1061-0022
IS - 3
ER -
ID: 36194691