Hy
Please, i would like to know how calculate the push forward $(\chi_j k_j)_{*}(\varphi_j u)$ according to the fragment of paper that I put in the photo.
For me i have to use the push forward as a function in variables $(x,t)$ then $(\chi_j k_j)_{*}(\varphi_j u)(x,t)= \varphi_j u ((\chi_j k_j)^{-1}(x,t)) =\varphi_j u (k_{j}^{-1}(x,t)\chi_{j}^{-1}(x,t))=\varphi_j u (k_{j}^{-1}(x,t) (\frac{x}{\langle t\rangle},t))$ but i think that something is wrong because $k_j$ is defined on $\mathbb R^n$ or some subset of it. And if i compose $k_{j}^{-1}\circ \chi_{j}^{-1}(x,t)$ do not have sense again, so how can i calculate this? Or how interpretate this push forward. Sorry by confusion, somebody can help me please?
Thanks
