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Jan
24
accepted Why is the sign of $L^2$ opposite?
Jan
24
comment Why is the sign of $L^2$ opposite?
Great suggestion. I haven't come up with that idea!
Jan
24
comment Why is the sign of $L^2$ opposite?
I came up with this question, since I thought there would be some convention such that $L^2_x$ is defined as $L^t_xL_x$, which means multiplication of the transposed matrix and the original one. Otherwise the identity doesn't seem to hold. Likewise, if I don't assume the above convention, Casimir element of $\mathcal{so(3)}$ becomes $-\frac{1}{2}(L^2_x+L^2_y+L^2_z)$, which has an incorrect sign.
Jan
24
asked Why is the sign of $L^2$ opposite?
Jan
23
comment Fubini's theorem for finite dimensional vector space?
I didn't think that Haar measure would do the job in that way. Thanks a lot!
Jan
22
comment Fubini's theorem for finite dimensional vector space?
I'm sorry. I was considering about a Haar measure on $F^n$. It is nice that the standard isomorphism is measure-preserving. While it sounds obvious, I couldn't find it in my textbook. Thank you!
Jan
22
asked Fubini's theorem for finite dimensional vector space?
Jan
14
comment Calculation of commutator of Lie algebra for affine linear maps
It worked pretty good!
Jan
14
comment Calculation of commutator of Lie algebra for affine linear maps
That makes sense! Thanks a lot.
Jan
14
asked Calculation of commutator of Lie algebra for affine linear maps
Jan
14
comment Taylor series identity for polynomial using Lie group
That completely makes sense!
Jan
14
comment Taylor series identity for polynomial using Lie group
Sorry, but could you give me a hint for that hint?
Jan
14
asked Taylor series identity for polynomial using Lie group
Dec
31
comment Why did $Ext$ appear to make the sequence exact after taking its dual?
From your mention of the long exact sequence, I found an explicit formula of the relevant long exact sequence! Thanks so much.
Dec
31
asked Why did $Ext$ appear to make the sequence exact after taking its dual?
Nov
27
comment What are the sequels to Rudin's Functional Analysis?
Thanks for your suggestion. As almost a year passed since my post, I'm now interested in operator theory more. So, I will check the operator theory book you mentioned.
Nov
10
comment What is the topology of smooth immersed submanifold?
Thanks for your answer. Your advice enabled me to solve the exercise!
Nov
10
asked What is the topology of smooth immersed submanifold?
Oct
10
comment If $f\in C^{\infty}$, $f$ is in Schwarz space iff $x^{\beta}\partial^{\alpha}f$ is bounded for $\forall \alpha, \beta$.
Thanks for your clarification! I think $\delta^{-1}\geq 1$, so the last term can be just modified $2^N\to 2^{N+1}$ as well.
Oct
10
accepted If $f\in C^{\infty}$, $f$ is in Schwarz space iff $x^{\beta}\partial^{\alpha}f$ is bounded for $\forall \alpha, \beta$.