Solving doubleintegral $intint f(g(x,y)) dy dx$ over annulus $D$ in $R^2$ where $g$ is Isometry
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I want to solve certain triple integral $intint f(g(x,y)) dy dx$ over annulus $D$ (concentric about origin) in $R^2$ where $g$ is an Isometry of a plane and $f$ is a given function. Because of the symmetry of annulus, does it suffices to only solve the integral when $g$ is a translation? I think this because the effect of other three symmetrices can be viewed just as the special cases of translation for annulus, is that roght?
real-analysis calculus geometry euclidean-geometry symmetric-groups
asked Jan 7 at 23:19
ershersh
275112
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add a comment |
$begingroup$
I want to solve certain triple integral $intint f(g(x,y)) dy dx$ over annulus $D$ (concentric about origin) in $R^2$ where $g$ is an Isometry of a plane and $f$ is a given function. Because of the symmetry of annulus, does it suffices to only solve the integral when $g$ is a translation? I think this because the effect of other three symmetrices can be viewed just as the special cases of translation for annulus, is that roght?
real-analysis calculus geometry euclidean-geometry symmetric-groups
asked Jan 7 at 23:19
ershersh
275112
$endgroup$
add a comment |
$begingroup$
I want to solve certain triple integral $intint f(g(x,y)) dy dx$ over annulus $D$ (concentric about origin) in $R^2$ where $g$ is an Isometry of a plane and $f$ is a given function. Because of the symmetry of annulus, does it suffices to only solve the integral when $g$ is a translation? I think this because the effect of other three symmetrices can be viewed just as the special cases of translation for annulus, is that roght?
real-analysis calculus geometry euclidean-geometry symmetric-groups
asked Jan 7 at 23:19
ershersh
275112
$endgroup$
I want to solve certain triple integral $intint f(g(x,y)) dy dx$ over annulus $D$ (concentric about origin) in $R^2$ where $g$ is an Isometry of a plane and $f$ is a given function. Because of the symmetry of annulus, does it suffices to only solve the integral when $g$ is a translation? I think this because the effect of other three symmetrices can be viewed just as the special cases of translation for annulus, is that roght?
real-analysis calculus geometry euclidean-geometry symmetric-groups
real-analysis calculus geometry euclidean-geometry symmetric-groups
asked Jan 7 at 23:19
ershersh
275112
asked Jan 7 at 23:19
ershersh
275112
edited Jan 8 at 3:57
ersh
asked Jan 7 at 23:19
ershersh
275112
asked Jan 7 at 23:19
ershersh
275112
asked Jan 7 at 23:19
ershersh
275112
275112
add a comment |
add a comment |
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