An accurate asymptotic estimate for the trace of the heat kernel of a -pseudo-differential operator

Key Points

• An optimal error bound is established for the asymptotic estimate of the heat kernel trace.
• The results provide a refinement of previous findings by Nicola and Rodino, enhancing mathematical precision.
• This study focuses on elliptic operators, crucial for understanding heat equations in mathematical physics.
• The asymptotic formula offers insights relevant to applications in differential equations and spectral theory.