How do I show a function $f$ belongs to $C_0^infty(mathbb{R^n})$ [on hold]
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How do I show that $f$ belongs to $C_0^infty(mathbb{R^n})$ ?
$$
f(x) = left{begin{array}{lc}expleft(-dfrac{1}{1-|x|^2}right) & |x|<1 \ 0 & |x|geq 1 end{array}right.
$$
functional-analysis analysis exponential-function
edited Dec 1 at 13:43
amWhy
191k27223439
asked Dec 1 at 12:06
M. Berns
392
put on hold as off-topic by user10354138, Qmechanic, user302797, RRL, Martin Sleziak Dec 1 at 15:37
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Qmechanic, user302797, RRL, Martin Sleziak
If this question can be reworded to fit the rules in the help center, please edit the question.
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show 1 more comment
up vote
0
down vote
favorite
How do I show that $f$ belongs to $C_0^infty(mathbb{R^n})$ ?
$$
f(x) = left{begin{array}{lc}expleft(-dfrac{1}{1-|x|^2}right) & |x|<1 \ 0 & |x|geq 1 end{array}right.
$$
functional-analysis analysis exponential-function
edited Dec 1 at 13:43
amWhy
191k27223439
asked Dec 1 at 12:06
M. Berns
392
put on hold as off-topic by user10354138, Qmechanic, user302797, RRL, Martin Sleziak Dec 1 at 15:37
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Qmechanic, user302797, RRL, Martin Sleziak
If this question can be reworded to fit the rules in the help center, please edit the question.
2
you look elsewhere on MSE because this has probably been asked a lot
– mathworker21
Dec 1 at 12:09
2
also, your definition is weird. it never holds that $|x| < 0$.
– mathworker21
Dec 1 at 12:09
@mathworker21 I already tried to find it here but unfortunately there were no question like that ..
– M. Berns
Dec 1 at 12:20
Srry I made like mathworker21 said abig mistake in my definition. It clearly has to be a 1 instead of the 0. Edit is done.
– M. Berns
Dec 1 at 12:41
I found at least this, maybe somebody can find other questions about this function: Prove $f(x) in C^infty$.
– Martin Sleziak
Dec 1 at 15:41
|
show 1 more comment
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How do I show that $f$ belongs to $C_0^infty(mathbb{R^n})$ ?
$$
f(x) = left{begin{array}{lc}expleft(-dfrac{1}{1-|x|^2}right) & |x|<1 \ 0 & |x|geq 1 end{array}right.
$$
functional-analysis analysis exponential-function
edited Dec 1 at 13:43
amWhy
191k27223439
asked Dec 1 at 12:06
M. Berns
392
How do I show that $f$ belongs to $C_0^infty(mathbb{R^n})$ ?
$$
f(x) = left{begin{array}{lc}expleft(-dfrac{1}{1-|x|^2}right) & |x|<1 \ 0 & |x|geq 1 end{array}right.
$$
functional-analysis analysis exponential-function
functional-analysis analysis exponential-function
edited Dec 1 at 13:43
amWhy
191k27223439
asked Dec 1 at 12:06
M. Berns
392
edited Dec 1 at 13:43
amWhy
191k27223439
asked Dec 1 at 12:06
M. Berns
392
edited Dec 1 at 13:43
amWhy
191k27223439
edited Dec 1 at 13:43
amWhy
191k27223439
edited Dec 1 at 13:43
amWhy
191k27223439
191k27223439
asked Dec 1 at 12:06
M. Berns
392
asked Dec 1 at 12:06
M. Berns
392
asked Dec 1 at 12:06
M. Berns
392
392
put on hold as off-topic by user10354138, Qmechanic, user302797, RRL, Martin Sleziak Dec 1 at 15:37
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Qmechanic, user302797, RRL, Martin Sleziak
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by user10354138, Qmechanic, user302797, RRL, Martin Sleziak Dec 1 at 15:37
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, Qmechanic, user302797, RRL, Martin Sleziak
If this question can be reworded to fit the rules in the help center, please edit the question.
2
you look elsewhere on MSE because this has probably been asked a lot
– mathworker21
Dec 1 at 12:09
2
also, your definition is weird. it never holds that $|x| < 0$.
– mathworker21
Dec 1 at 12:09
@mathworker21 I already tried to find it here but unfortunately there were no question like that ..
– M. Berns
Dec 1 at 12:20
Srry I made like mathworker21 said abig mistake in my definition. It clearly has to be a 1 instead of the 0. Edit is done.
– M. Berns
Dec 1 at 12:41
I found at least this, maybe somebody can find other questions about this function: Prove $f(x) in C^infty$.
– Martin Sleziak
Dec 1 at 15:41
|
show 1 more comment
2
you look elsewhere on MSE because this has probably been asked a lot
– mathworker21
Dec 1 at 12:09
2
also, your definition is weird. it never holds that $|x| < 0$.
– mathworker21
Dec 1 at 12:09
@mathworker21 I already tried to find it here but unfortunately there were no question like that ..
– M. Berns
Dec 1 at 12:20
Srry I made like mathworker21 said abig mistake in my definition. It clearly has to be a 1 instead of the 0. Edit is done.
– M. Berns
Dec 1 at 12:41
I found at least this, maybe somebody can find other questions about this function: Prove $f(x) in C^infty$.
– Martin Sleziak
Dec 1 at 15:41
2
2
you look elsewhere on MSE because this has probably been asked a lot
– mathworker21
Dec 1 at 12:09
you look elsewhere on MSE because this has probably been asked a lot
– mathworker21
Dec 1 at 12:09
2
2
also, your definition is weird. it never holds that $|x| < 0$.
– mathworker21
Dec 1 at 12:09
also, your definition is weird. it never holds that $|x| < 0$.
– mathworker21
Dec 1 at 12:09
@mathworker21 I already tried to find it here but unfortunately there were no question like that ..
– M. Berns
Dec 1 at 12:20
@mathworker21 I already tried to find it here but unfortunately there were no question like that ..
– M. Berns
Dec 1 at 12:20
Srry I made like mathworker21 said abig mistake in my definition. It clearly has to be a 1 instead of the 0. Edit is done.
– M. Berns
Dec 1 at 12:41
Srry I made like mathworker21 said abig mistake in my definition. It clearly has to be a 1 instead of the 0. Edit is done.
– M. Berns
Dec 1 at 12:41
I found at least this, maybe somebody can find other questions about this function: Prove $f(x) in C^infty$.
– Martin Sleziak
Dec 1 at 15:41
I found at least this, maybe somebody can find other questions about this function: Prove $f(x) in C^infty$.
– Martin Sleziak
Dec 1 at 15:41
|
show 1 more comment
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2
you look elsewhere on MSE because this has probably been asked a lot
– mathworker21
Dec 1 at 12:09
2
also, your definition is weird. it never holds that $|x| < 0$.
– mathworker21
Dec 1 at 12:09
@mathworker21 I already tried to find it here but unfortunately there were no question like that ..
– M. Berns
Dec 1 at 12:20
Srry I made like mathworker21 said abig mistake in my definition. It clearly has to be a 1 instead of the 0. Edit is done.
– M. Berns
Dec 1 at 12:41
I found at least this, maybe somebody can find other questions about this function: Prove $f(x) in C^infty$.
– Martin Sleziak
Dec 1 at 15:41