Mixing
What does $sim_k$ mean
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I am reading the following lecture notes:(http://www.math.ucla.edu/~tao/247b.1.07w/notes8.pdf) regarding stationary phase integrals, specifically concerned with their asymptotic behavior and there is this symbol $sim_k$ that keeps popping up. I understand what the similarity symbol means, but the subscript $k$ is slightly confusing me since I've never seen it before and I can't find anywhere online that describes the meaning. To give some context in case there are multiple meanings, this symbol is mostly used when giving size estimates such as
$$
|c_0| sim_k |phi^{(k)}(x_0)|^{-1/k}|a(x_0)|
$$
for some integer $k geq 2$, $phi$ and $a$ are smooth functions.
For reference, this symbol occurs in Lemma 2.5 and Lemma 2.6 in the lectures notes that I linked.
Cheers in advance for any help.
analysis notation asymptotics
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
$endgroup$
add a comment |
$begingroup$
I am reading the following lecture notes:(http://www.math.ucla.edu/~tao/247b.1.07w/notes8.pdf) regarding stationary phase integrals, specifically concerned with their asymptotic behavior and there is this symbol $sim_k$ that keeps popping up. I understand what the similarity symbol means, but the subscript $k$ is slightly confusing me since I've never seen it before and I can't find anywhere online that describes the meaning. To give some context in case there are multiple meanings, this symbol is mostly used when giving size estimates such as
$$
|c_0| sim_k |phi^{(k)}(x_0)|^{-1/k}|a(x_0)|
$$
for some integer $k geq 2$, $phi$ and $a$ are smooth functions.
For reference, this symbol occurs in Lemma 2.5 and Lemma 2.6 in the lectures notes that I linked.
Cheers in advance for any help.
analysis notation asymptotics
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
$endgroup$
$begingroup$
Without knowing where you encountered this, we have no way to tell you what it means. It is likely that it is defined somewhere in what you are reading.
$endgroup$
– Morgan Rodgers
Jan 14 at 2:50
$begingroup$
I think this notation usually means the "similarity symbol" where the two constants depending only on k.
$endgroup$
– Zixiao_Liu
Jan 14 at 2:56
$begingroup$
Thanks, I didn't think of that. I added a link to what I'm reading.
$endgroup$
– Jandré Snyman
Jan 14 at 2:57
add a comment |
$begingroup$
I am reading the following lecture notes:(http://www.math.ucla.edu/~tao/247b.1.07w/notes8.pdf) regarding stationary phase integrals, specifically concerned with their asymptotic behavior and there is this symbol $sim_k$ that keeps popping up. I understand what the similarity symbol means, but the subscript $k$ is slightly confusing me since I've never seen it before and I can't find anywhere online that describes the meaning. To give some context in case there are multiple meanings, this symbol is mostly used when giving size estimates such as
$$
|c_0| sim_k |phi^{(k)}(x_0)|^{-1/k}|a(x_0)|
$$
for some integer $k geq 2$, $phi$ and $a$ are smooth functions.
For reference, this symbol occurs in Lemma 2.5 and Lemma 2.6 in the lectures notes that I linked.
Cheers in advance for any help.
analysis notation asymptotics
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
$endgroup$
I am reading the following lecture notes:(http://www.math.ucla.edu/~tao/247b.1.07w/notes8.pdf) regarding stationary phase integrals, specifically concerned with their asymptotic behavior and there is this symbol $sim_k$ that keeps popping up. I understand what the similarity symbol means, but the subscript $k$ is slightly confusing me since I've never seen it before and I can't find anywhere online that describes the meaning. To give some context in case there are multiple meanings, this symbol is mostly used when giving size estimates such as
$$
|c_0| sim_k |phi^{(k)}(x_0)|^{-1/k}|a(x_0)|
$$
for some integer $k geq 2$, $phi$ and $a$ are smooth functions.
For reference, this symbol occurs in Lemma 2.5 and Lemma 2.6 in the lectures notes that I linked.
Cheers in advance for any help.
analysis notation asymptotics
analysis notation asymptotics
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
edited Jan 14 at 2:57
Jandré Snyman
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
asked Jan 14 at 2:47
Jandré SnymanJandré Snyman
17410
17410
$begingroup$
Without knowing where you encountered this, we have no way to tell you what it means. It is likely that it is defined somewhere in what you are reading.
$endgroup$
– Morgan Rodgers
Jan 14 at 2:50
$begingroup$
I think this notation usually means the "similarity symbol" where the two constants depending only on k.
$endgroup$
– Zixiao_Liu
Jan 14 at 2:56
$begingroup$
Thanks, I didn't think of that. I added a link to what I'm reading.
$endgroup$
– Jandré Snyman
Jan 14 at 2:57
add a comment |
$begingroup$
Without knowing where you encountered this, we have no way to tell you what it means. It is likely that it is defined somewhere in what you are reading.
$endgroup$
– Morgan Rodgers
Jan 14 at 2:50
$begingroup$
I think this notation usually means the "similarity symbol" where the two constants depending only on k.
$endgroup$
– Zixiao_Liu
Jan 14 at 2:56
$begingroup$
Thanks, I didn't think of that. I added a link to what I'm reading.
$endgroup$
– Jandré Snyman
Jan 14 at 2:57
$begingroup$
Without knowing where you encountered this, we have no way to tell you what it means. It is likely that it is defined somewhere in what you are reading.
$endgroup$
– Morgan Rodgers
Jan 14 at 2:50
$begingroup$
Without knowing where you encountered this, we have no way to tell you what it means. It is likely that it is defined somewhere in what you are reading.
$endgroup$
– Morgan Rodgers
Jan 14 at 2:50
$begingroup$
I think this notation usually means the "similarity symbol" where the two constants depending only on k.
$endgroup$
– Zixiao_Liu
Jan 14 at 2:56
$begingroup$
I think this notation usually means the "similarity symbol" where the two constants depending only on k.
$endgroup$
– Zixiao_Liu
Jan 14 at 2:56
$begingroup$
Thanks, I didn't think of that. I added a link to what I'm reading.
$endgroup$
– Jandré Snyman
Jan 14 at 2:57
$begingroup$
Thanks, I didn't think of that. I added a link to what I'm reading.
$endgroup$
– Jandré Snyman
Jan 14 at 2:57
add a comment |
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$begingroup$
Without knowing where you encountered this, we have no way to tell you what it means. It is likely that it is defined somewhere in what you are reading.
$endgroup$
– Morgan Rodgers
Jan 14 at 2:50
$begingroup$
I think this notation usually means the "similarity symbol" where the two constants depending only on k.
$endgroup$
– Zixiao_Liu
Jan 14 at 2:56
$begingroup$
Thanks, I didn't think of that. I added a link to what I'm reading.
$endgroup$
– Jandré Snyman
Jan 14 at 2:57