Theoretical Statistics and Mathematics Unit, ISI Delhi

August 31, 2018 (Friday) ,
3:30 PM at Webinar

Speaker:
K. B. Sinha,
JNCASR, Bengaluru

Title:
Trace formula in two operator variables - extension of Krein’s formula

Abstract of Talk

Krein's trace formula asserts that for two self-adjoint operators $H$ and $H_0$ in an infinite dimensional Hilbert space with $H - H_0$ trace-class, $\phi(H) - \phi(H_0)$ is trace-class and its trace can be expressed as an integral of $\phi'$ by a measure on $\mathbb{R}$, which is absolutely continuous with respect to the Lebesgue measure, where $\phi$ is a ``nice'' function. This expression has a geometric interpretation and its natural extension to more than one dimension ($2-d$) as per Connes' prescription leads to a similar integral formula with a measure, which in general, is not absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}^2$.