dilation operator on $L^2(mathbbR)$ is continuous
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Prove the statement let $D:mathbbR^+rightarrow L^2(mathbbR)$ defined by $D(a)=f_a$ and $f_a(x)=frac1sqrtaf(fracxa)$, where $fin L^2(mathbbR)$ then the mapping $D$ is continuous on $mathbbR^+.$
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Prove the statement let $D:mathbbR^+rightarrow L^2(mathbbR)$ defined by $D(a)=f_a$ and $f_a(x)=frac1sqrtaf(fracxa)$, where $fin L^2(mathbbR)$ then the mapping $D$ is continuous on $mathbbR^+.$
wavelets
Why is this tagged as "wavelets" ? Plus, you should show some efforts if you want someone to help you.
â nicomezi
Aug 29 at 6:04
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up vote
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up vote
0
down vote
favorite
Prove the statement let $D:mathbbR^+rightarrow L^2(mathbbR)$ defined by $D(a)=f_a$ and $f_a(x)=frac1sqrtaf(fracxa)$, where $fin L^2(mathbbR)$ then the mapping $D$ is continuous on $mathbbR^+.$
wavelets
Prove the statement let $D:mathbbR^+rightarrow L^2(mathbbR)$ defined by $D(a)=f_a$ and $f_a(x)=frac1sqrtaf(fracxa)$, where $fin L^2(mathbbR)$ then the mapping $D$ is continuous on $mathbbR^+.$
wavelets
wavelets
edited Sep 7 at 6:20
asked Aug 29 at 5:59
kamalakkannan
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94
Why is this tagged as "wavelets" ? Plus, you should show some efforts if you want someone to help you.
â nicomezi
Aug 29 at 6:04
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Why is this tagged as "wavelets" ? Plus, you should show some efforts if you want someone to help you.
â nicomezi
Aug 29 at 6:04
Why is this tagged as "wavelets" ? Plus, you should show some efforts if you want someone to help you.
â nicomezi
Aug 29 at 6:04
Why is this tagged as "wavelets" ? Plus, you should show some efforts if you want someone to help you.
â nicomezi
Aug 29 at 6:04
add a comment |Â
1 Answer
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Yes. You can approximate $f$ by a continuous function $g$ whose support is a compact subset of $(0,infty)$ and it is fairly starightforward to verify continuity of $a to g_a$. (The given function becomes a uniform limit of continuous functions).
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Yes. You can approximate $f$ by a continuous function $g$ whose support is a compact subset of $(0,infty)$ and it is fairly starightforward to verify continuity of $a to g_a$. (The given function becomes a uniform limit of continuous functions).
add a comment |Â
up vote
1
down vote
Yes. You can approximate $f$ by a continuous function $g$ whose support is a compact subset of $(0,infty)$ and it is fairly starightforward to verify continuity of $a to g_a$. (The given function becomes a uniform limit of continuous functions).
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Yes. You can approximate $f$ by a continuous function $g$ whose support is a compact subset of $(0,infty)$ and it is fairly starightforward to verify continuity of $a to g_a$. (The given function becomes a uniform limit of continuous functions).
Yes. You can approximate $f$ by a continuous function $g$ whose support is a compact subset of $(0,infty)$ and it is fairly starightforward to verify continuity of $a to g_a$. (The given function becomes a uniform limit of continuous functions).
answered Aug 29 at 6:07
Kavi Rama Murthy
26.7k31438
26.7k31438
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Why is this tagged as "wavelets" ? Plus, you should show some efforts if you want someone to help you.
â nicomezi
Aug 29 at 6:04