Constructing a Schwartzfunction
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Hi I am working on a problem and as a hint I received the following:
Construct a Schwartz function $phi in mathscr s (mathbb R^n) $which disappears outside a neighbourhood P but $phi (x) = 1$ for $x in P$. However this confuses me, since the definition of a Schwartz space is that the function has to be in $C^{infty}$. And if I define $forall x in P: phi(x) = 1$ and $forall x notin P: phi(x) = 0$, then $phi notin C^{infty}$
Thank you for the help
schwartz-space
asked Dec 8 '18 at 14:37
JamesJames
324
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add a comment |
$begingroup$
Hi I am working on a problem and as a hint I received the following:
Construct a Schwartz function $phi in mathscr s (mathbb R^n) $which disappears outside a neighbourhood P but $phi (x) = 1$ for $x in P$. However this confuses me, since the definition of a Schwartz space is that the function has to be in $C^{infty}$. And if I define $forall x in P: phi(x) = 1$ and $forall x notin P: phi(x) = 0$, then $phi notin C^{infty}$
Thank you for the help
schwartz-space
asked Dec 8 '18 at 14:37
JamesJames
324
$endgroup$
1
$begingroup$
Notice that $phi$ should vanish outside of a neighbourhood of $P$, so you have some room to make it drop down to zero smoothly.
$endgroup$
– MisterRiemann
Dec 8 '18 at 14:40
add a comment |
$begingroup$
Hi I am working on a problem and as a hint I received the following:
Construct a Schwartz function $phi in mathscr s (mathbb R^n) $which disappears outside a neighbourhood P but $phi (x) = 1$ for $x in P$. However this confuses me, since the definition of a Schwartz space is that the function has to be in $C^{infty}$. And if I define $forall x in P: phi(x) = 1$ and $forall x notin P: phi(x) = 0$, then $phi notin C^{infty}$
Thank you for the help
schwartz-space
asked Dec 8 '18 at 14:37
JamesJames
324
$endgroup$
Hi I am working on a problem and as a hint I received the following:
Construct a Schwartz function $phi in mathscr s (mathbb R^n) $which disappears outside a neighbourhood P but $phi (x) = 1$ for $x in P$. However this confuses me, since the definition of a Schwartz space is that the function has to be in $C^{infty}$. And if I define $forall x in P: phi(x) = 1$ and $forall x notin P: phi(x) = 0$, then $phi notin C^{infty}$
Thank you for the help
schwartz-space
schwartz-space
asked Dec 8 '18 at 14:37
JamesJames
324
asked Dec 8 '18 at 14:37
JamesJames
324
asked Dec 8 '18 at 14:37
JamesJames
324
asked Dec 8 '18 at 14:37
JamesJames
324
asked Dec 8 '18 at 14:37
JamesJames
324
324
1
$begingroup$
Notice that $phi$ should vanish outside of a neighbourhood of $P$, so you have some room to make it drop down to zero smoothly.
$endgroup$
– MisterRiemann
Dec 8 '18 at 14:40
add a comment |
1
$begingroup$
Notice that $phi$ should vanish outside of a neighbourhood of $P$, so you have some room to make it drop down to zero smoothly.
$endgroup$
– MisterRiemann
Dec 8 '18 at 14:40
1
1
$begingroup$
Notice that $phi$ should vanish outside of a neighbourhood of $P$, so you have some room to make it drop down to zero smoothly.
$endgroup$
– MisterRiemann
Dec 8 '18 at 14:40
$begingroup$
Notice that $phi$ should vanish outside of a neighbourhood of $P$, so you have some room to make it drop down to zero smoothly.
$endgroup$
– MisterRiemann
Dec 8 '18 at 14:40
add a comment |
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$begingroup$
Notice that $phi$ should vanish outside of a neighbourhood of $P$, so you have some room to make it drop down to zero smoothly.
$endgroup$
– MisterRiemann
Dec 8 '18 at 14:40