balugaa
Feb21-11, 05:51 PM
Working through this proof .. which has the following step
\int\limits_{S^{n-1}}\int_0^\infty |\hat{f}(\sigma\theta)|^2(1+\sigma^2)^{s+1/2}\mathrm{d}\sigma\mathrm{d}\theta
Then we have the change of variable i.e. \psi=(\theta\sigma)
to give
\int\limits_{R^2}|\psi|^{-1}(1+|\psi|^2)^{s+1/2}|\hat{f}(\psi)|^2d\psi
Now i figure the
\psi^-1
is a result of the change of variable in the integration of d_sigma and d_theta,
Could anyone explain how the 1+psi terms comes to be .. by my working i had that as 1+psi/theta
Sorry but my texing may of gone out of whack
\int\limits_{S^{n-1}}\int_0^\infty |\hat{f}(\sigma\theta)|^2(1+\sigma^2)^{s+1/2}\mathrm{d}\sigma\mathrm{d}\theta
Then we have the change of variable i.e. \psi=(\theta\sigma)
to give
\int\limits_{R^2}|\psi|^{-1}(1+|\psi|^2)^{s+1/2}|\hat{f}(\psi)|^2d\psi
Now i figure the
\psi^-1
is a result of the change of variable in the integration of d_sigma and d_theta,
Could anyone explain how the 1+psi terms comes to be .. by my working i had that as 1+psi/theta
Sorry but my texing may of gone out of whack