Properties of delta function
$begingroup$
Consider two arbitrary sets of coordinates $z_0$ and $z$ in some space, mapped via some
$bar{z} :$=$z_0 rightarrow z$
I have a function
$$tag{1}rho(z)=intdelta(z-bar{z}(z_0))rho_0 (z_0)dz_0$$
this will give me
$$tag{2}rho(z)=rho_0 (bar{z}^{-1}(z))frac{partial z_0}{partial z}$$
How to obtain equation (2) from equation (1).
distribution-theory dirac-delta
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
$endgroup$
add a comment |
$begingroup$
Consider two arbitrary sets of coordinates $z_0$ and $z$ in some space, mapped via some
$bar{z} :$=$z_0 rightarrow z$
I have a function
$$tag{1}rho(z)=intdelta(z-bar{z}(z_0))rho_0 (z_0)dz_0$$
this will give me
$$tag{2}rho(z)=rho_0 (bar{z}^{-1}(z))frac{partial z_0}{partial z}$$
How to obtain equation (2) from equation (1).
distribution-theory dirac-delta
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
$endgroup$
$begingroup$
This should be what you are looking for; math.stackexchange.com/q/56939/8157
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:40
$begingroup$
Also, please use the double dollar and the "tag" command for display formulas, instead of ------ Click on "edit" to see how I have done.
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:42
add a comment |
$begingroup$
Consider two arbitrary sets of coordinates $z_0$ and $z$ in some space, mapped via some
$bar{z} :$=$z_0 rightarrow z$
I have a function
$$tag{1}rho(z)=intdelta(z-bar{z}(z_0))rho_0 (z_0)dz_0$$
this will give me
$$tag{2}rho(z)=rho_0 (bar{z}^{-1}(z))frac{partial z_0}{partial z}$$
How to obtain equation (2) from equation (1).
distribution-theory dirac-delta
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
$endgroup$
Consider two arbitrary sets of coordinates $z_0$ and $z$ in some space, mapped via some
$bar{z} :$=$z_0 rightarrow z$
I have a function
$$tag{1}rho(z)=intdelta(z-bar{z}(z_0))rho_0 (z_0)dz_0$$
this will give me
$$tag{2}rho(z)=rho_0 (bar{z}^{-1}(z))frac{partial z_0}{partial z}$$
How to obtain equation (2) from equation (1).
distribution-theory dirac-delta
distribution-theory dirac-delta
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
edited Dec 17 '18 at 10:41
Giuseppe Negro
17.4k332126
17.4k332126
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
asked Dec 17 '18 at 10:28
Hari KrishnanHari Krishnan
243
243
$begingroup$
This should be what you are looking for; math.stackexchange.com/q/56939/8157
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:40
$begingroup$
Also, please use the double dollar and the "tag" command for display formulas, instead of ------ Click on "edit" to see how I have done.
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:42
add a comment |
$begingroup$
This should be what you are looking for; math.stackexchange.com/q/56939/8157
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:40
$begingroup$
Also, please use the double dollar and the "tag" command for display formulas, instead of ------ Click on "edit" to see how I have done.
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:42
$begingroup$
This should be what you are looking for; math.stackexchange.com/q/56939/8157
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:40
$begingroup$
This should be what you are looking for; math.stackexchange.com/q/56939/8157
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:40
$begingroup$
Also, please use the double dollar and the "tag" command for display formulas, instead of ------ Click on "edit" to see how I have done.
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:42
$begingroup$
Also, please use the double dollar and the "tag" command for display formulas, instead of ------ Click on "edit" to see how I have done.
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:42
add a comment |
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$begingroup$
This should be what you are looking for; math.stackexchange.com/q/56939/8157
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:40
$begingroup$
Also, please use the double dollar and the "tag" command for display formulas, instead of ------ Click on "edit" to see how I have done.
$endgroup$
– Giuseppe Negro
Dec 17 '18 at 10:42