All Questions

Consider a generalised harmonic oscillator of the form $$ A(x,D_x) = \langle x \rangle (1-\Delta_x)\langle x \rangle, \quad x \in \mathbb{R}^n, $$ where $\langle x \rangle = (1+|x|^2)^{1/2}.$ The ...

Let $D$ be the transverse signature operator constructed by Connes and Moscovici in the paper "Local index formula in Noncommutative Geometry":this is first order hypoelliptic pseudodifferential ...

Let $E\rightarrow X$ be a line bundle over a compact Riemann surface. Let $\Delta_{E}$ be the Dolbeault Laplacian $\Delta_{\overline{\partial}}$ extended to sections of $E$. Let $g_1, g_2$ be two ...

I have recently started to study the book "Fourier integrals in classical analysis " by Sogge mainly oscillatory integral decay methods. I have a question from the chapters 4 and 5. Mainly ...