Does such a test function exist?
0
$begingroup$
Is there a nonnegative test function $phi$ in $mathbb{R}^{n}$ such that
$Deltaphi(x/n)toDeltaphi(0) $ uniformly on bounded sets, as $ntoinfty$ ($Delta$ is the laplacian)
$Deltaphi(0) $ is not zero?
real-analysis distribution-theory
edited Dec 18 '18 at 19:55
Bernard
123k741117
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
$endgroup$
|
show 1 more comment
0
$begingroup$
Is there a nonnegative test function $phi$ in $mathbb{R}^{n}$ such that
$Deltaphi(x/n)toDeltaphi(0) $ uniformly on bounded sets, as $ntoinfty$ ($Delta$ is the laplacian)
$Deltaphi(0) $ is not zero?
real-analysis distribution-theory
edited Dec 18 '18 at 19:55
Bernard
123k741117
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
$endgroup$
$begingroup$
how can a function be in $mathbb{R}^n$?
$endgroup$
– gt6989b
Dec 18 '18 at 19:50
$begingroup$
This is hard to read. here is a good tutorial on formatting for this site.
$endgroup$
– lulu
Dec 18 '18 at 19:52
$begingroup$
lulu. Sorry! Bernard. Thanks for correction. gty98b. This is a smooth function with compact support.
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:03
1
$begingroup$
Any test function with $Delta phi(0)ne 0$ is an example (PS: you are using $n$ in different ways)
$endgroup$
– zhw.
Dec 18 '18 at 20:14
$begingroup$
But why the convergence whould be uniform?
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:49
|
show 1 more comment
0
0
0
$begingroup$
Is there a nonnegative test function $phi$ in $mathbb{R}^{n}$ such that
$Deltaphi(x/n)toDeltaphi(0) $ uniformly on bounded sets, as $ntoinfty$ ($Delta$ is the laplacian)
$Deltaphi(0) $ is not zero?
real-analysis distribution-theory
edited Dec 18 '18 at 19:55
Bernard
123k741117
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
$endgroup$
Is there a nonnegative test function $phi$ in $mathbb{R}^{n}$ such that
$Deltaphi(x/n)toDeltaphi(0) $ uniformly on bounded sets, as $ntoinfty$ ($Delta$ is the laplacian)
$Deltaphi(0) $ is not zero?
real-analysis distribution-theory
real-analysis distribution-theory
edited Dec 18 '18 at 19:55
Bernard
123k741117
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
edited Dec 18 '18 at 19:55
Bernard
123k741117
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
edited Dec 18 '18 at 19:55
Bernard
123k741117
edited Dec 18 '18 at 19:55
Bernard
123k741117
edited Dec 18 '18 at 19:55
Bernard
123k741117
123k741117
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
asked Dec 18 '18 at 19:48
M. RahmatM. Rahmat
291212
291212
$begingroup$
how can a function be in $mathbb{R}^n$?
$endgroup$
– gt6989b
Dec 18 '18 at 19:50
$begingroup$
This is hard to read. here is a good tutorial on formatting for this site.
$endgroup$
– lulu
Dec 18 '18 at 19:52
$begingroup$
lulu. Sorry! Bernard. Thanks for correction. gty98b. This is a smooth function with compact support.
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:03
1
$begingroup$
Any test function with $Delta phi(0)ne 0$ is an example (PS: you are using $n$ in different ways)
$endgroup$
– zhw.
Dec 18 '18 at 20:14
$begingroup$
But why the convergence whould be uniform?
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:49
|
show 1 more comment
$begingroup$
how can a function be in $mathbb{R}^n$?
$endgroup$
– gt6989b
Dec 18 '18 at 19:50
$begingroup$
This is hard to read. here is a good tutorial on formatting for this site.
$endgroup$
– lulu
Dec 18 '18 at 19:52
$begingroup$
lulu. Sorry! Bernard. Thanks for correction. gty98b. This is a smooth function with compact support.
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:03
1
$begingroup$
Any test function with $Delta phi(0)ne 0$ is an example (PS: you are using $n$ in different ways)
$endgroup$
– zhw.
Dec 18 '18 at 20:14
$begingroup$
But why the convergence whould be uniform?
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:49
$begingroup$
how can a function be in $mathbb{R}^n$?
$endgroup$
– gt6989b
Dec 18 '18 at 19:50
$begingroup$
how can a function be in $mathbb{R}^n$?
$endgroup$
– gt6989b
Dec 18 '18 at 19:50
$begingroup$
This is hard to read. here is a good tutorial on formatting for this site.
$endgroup$
– lulu
Dec 18 '18 at 19:52
$begingroup$
This is hard to read. here is a good tutorial on formatting for this site.
$endgroup$
– lulu
Dec 18 '18 at 19:52
$begingroup$
lulu. Sorry! Bernard. Thanks for correction. gty98b. This is a smooth function with compact support.
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:03
$begingroup$
lulu. Sorry! Bernard. Thanks for correction. gty98b. This is a smooth function with compact support.
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:03
1
1
$begingroup$
Any test function with $Delta phi(0)ne 0$ is an example (PS: you are using $n$ in different ways)
$endgroup$
– zhw.
Dec 18 '18 at 20:14
$begingroup$
Any test function with $Delta phi(0)ne 0$ is an example (PS: you are using $n$ in different ways)
$endgroup$
– zhw.
Dec 18 '18 at 20:14
$begingroup$
But why the convergence whould be uniform?
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:49
$begingroup$
But why the convergence whould be uniform?
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:49
|
show 1 more comment
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$begingroup$
how can a function be in $mathbb{R}^n$?
$endgroup$
– gt6989b
Dec 18 '18 at 19:50
$begingroup$
This is hard to read. here is a good tutorial on formatting for this site.
$endgroup$
– lulu
Dec 18 '18 at 19:52
$begingroup$
lulu. Sorry! Bernard. Thanks for correction. gty98b. This is a smooth function with compact support.
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:03
1
$begingroup$
Any test function with $Delta phi(0)ne 0$ is an example (PS: you are using $n$ in different ways)
$endgroup$
– zhw.
Dec 18 '18 at 20:14
$begingroup$
But why the convergence whould be uniform?
$endgroup$
– M. Rahmat
Dec 18 '18 at 20:49