Research Projects

The project focuses on studying multi-variable trace formulae on symmetric spaces, a fundamental theorem of integral calculus that should be more transparent in multi-variable contexts. Krein's trace formula and spectral shift function are fundamental results in perturbation theory, complementing the classical Taylor remainder formula. Anna Skripka proved the first and second-order trace formulas, Krein and Koplienko trace formulae, for a multivariate operator function under certain assumptions. The project aims to obtain Krein and Koplienko trace formulae in the multi-variable case for a larger class (Wiener class) of functions and to obtain an expression of higher-order trace formulas in the multi-variable case on symmetric spaces. The Taylor-like approximations remained unexplored in the multivariate case, despite being well investigated in the single-variable case.