Riesz transform representation on the torus
$begingroup$
Does anyone knows how to do the representation of the Riesz transform on the torus?
I know that on the space $mathbb{R}^d$, is it given by
$${displaystyle R_{j}f(x)=c_{d}lim _{epsilon to 0}int _{mathbf {R} ^{d}backslash B_{epsilon }(x)}{frac {(t_{j}-x_{j})f(t)}{|x-t|^{d+1}}},dt} $$
where $c_{d}={frac {1}{pi omega _{{d-1}}}}={frac {Gamma [(d+1)/2]}{pi ^{{(d+1)/2}}}}.$
real-analysis transformation
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
$endgroup$
add a comment |
$begingroup$
Does anyone knows how to do the representation of the Riesz transform on the torus?
I know that on the space $mathbb{R}^d$, is it given by
$${displaystyle R_{j}f(x)=c_{d}lim _{epsilon to 0}int _{mathbf {R} ^{d}backslash B_{epsilon }(x)}{frac {(t_{j}-x_{j})f(t)}{|x-t|^{d+1}}},dt} $$
where $c_{d}={frac {1}{pi omega _{{d-1}}}}={frac {Gamma [(d+1)/2]}{pi ^{{(d+1)/2}}}}.$
real-analysis transformation
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
$endgroup$
add a comment |
$begingroup$
Does anyone knows how to do the representation of the Riesz transform on the torus?
I know that on the space $mathbb{R}^d$, is it given by
$${displaystyle R_{j}f(x)=c_{d}lim _{epsilon to 0}int _{mathbf {R} ^{d}backslash B_{epsilon }(x)}{frac {(t_{j}-x_{j})f(t)}{|x-t|^{d+1}}},dt} $$
where $c_{d}={frac {1}{pi omega _{{d-1}}}}={frac {Gamma [(d+1)/2]}{pi ^{{(d+1)/2}}}}.$
real-analysis transformation
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
$endgroup$
Does anyone knows how to do the representation of the Riesz transform on the torus?
I know that on the space $mathbb{R}^d$, is it given by
$${displaystyle R_{j}f(x)=c_{d}lim _{epsilon to 0}int _{mathbf {R} ^{d}backslash B_{epsilon }(x)}{frac {(t_{j}-x_{j})f(t)}{|x-t|^{d+1}}},dt} $$
where $c_{d}={frac {1}{pi omega _{{d-1}}}}={frac {Gamma [(d+1)/2]}{pi ^{{(d+1)/2}}}}.$
real-analysis transformation
real-analysis transformation
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
asked Dec 18 '18 at 20:28
Pires DankanPires Dankan
208115
208115
add a comment |
add a comment |
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