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 -