TY - JOUR

T1 - Two-sided estimates for the trace of the difference of two semigroups

AU - Birman, M. Sh

AU - Sloushch, V. A.

PY - 2009/9

Y1 - 2009/9

N2 - This paper deals with the derivation of two-sided estimates for the trace of the difference of two semigroups generated by two Schrodinger operators in L (2)(a"e(3)) with trace class difference of the resolvents. Use is made of a purely operator-theoretic technique. The results are stated in a rather general abstract form. The sharpness of our estimates is confirmed by the fact that they imply the asymptotic behavior of the trace of the difference of the semigroups as t -> +0. Our considerations are substantially based on the Krein-Lifshits formula and on the Birman-Solomyak representation for the spectral shift function.

AB - This paper deals with the derivation of two-sided estimates for the trace of the difference of two semigroups generated by two Schrodinger operators in L (2)(a"e(3)) with trace class difference of the resolvents. Use is made of a purely operator-theoretic technique. The results are stated in a rather general abstract form. The sharpness of our estimates is confirmed by the fact that they imply the asymptotic behavior of the trace of the difference of the semigroups as t -> +0. Our considerations are substantially based on the Krein-Lifshits formula and on the Birman-Solomyak representation for the spectral shift function.

KW - spectral shift function

KW - Schrodinger operator

KW - trace formula

KW - FORMULA

U2 - 10.1007/s10688-009-0026-x

DO - 10.1007/s10688-009-0026-x

M3 - статья

VL - 43

SP - 184

EP - 189

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 3

ER -