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Oct
2 |
asked | Is there an elementary proof of the polar factorization theorem for vector-valued function? |
Sep
30 |
comment |
Regularity of decomposition of matrix-valued function
@AndrásBátkai: this can be seen from the spectral decomposition of positive definite matrix. Namely, write $A=\sum_{i=1}^n\lambda_i P_i(A)$, then $g(A)=\sum_{i=1}^ng(\lambda_i)P_i(A)$, which can be found in standard linear algebra book. Hope this helps. |
Sep
29 |
accepted | Regularity of decomposition of matrix-valued function |
Sep
29 |
comment |
Regularity of decomposition of matrix-valued function
@abx: Is there a simple proof of this fact without using diagonalization to diagonal matrix? |
Sep
29 |
answered | Are solutions of the Beltrami Equations necessarily smooth? |
Sep
29 |
revised |
Regularity of decomposition of matrix-valued function
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Sep
29 |
comment |
Regularity of decomposition of matrix-valued function
@abx: It is not very clear to me, see mathoverflow.net/questions/60533/… somewhat surprisingly. |
Sep
29 |
asked | Regularity of decomposition of matrix-valued function |
Sep
18 |
awarded | Yearling |
Apr
10 |
revised |
Are there any known ``topological" invariants for branched coverings?
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Apr
10 |
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Are there any known ``topological" invariants for branched coverings?
@AlexDegtyarev: Take the example as in the homeomorphism case, the linking number of circle and sphere are topological invariant, it can not change from +1 to -1 under a sense-preserving homeomorphism. I want a similar kind of concept, so that they are kept by branched coverings as defined above. |
Apr
10 |
comment |
Are there any known ``topological" invariants for branched coverings?
@AlexDegtyarev: (1) I noticed that there are different definitions of branched coverings used in different areas. In geometric function theory, one usually defines branched coverings as above and it is not necessarily to be a real covering mapping. (2) I corrected it in 3-dim and in 4 dim, one needs to use circle and sphere. (3). I want some concept defined topologically on $\Omega$ and it still makes senses in the target under the branched covering $f$ so that this concept are kept. |
Apr
10 |
revised |
Are there any known ``topological" invariants for branched coverings?
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Apr
10 |
asked | Are there any known ``topological" invariants for branched coverings? |
Apr
10 |
revised |
A lower-dimensional algebraic topology problem between homology group and fundamental group
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Apr
8 |
comment |
Should one post a paper on the arXiv if it is not intended to be published?
I think another good way is to establish a personal homepage and then put it up there as a small notes indicating what it is about. At least, many well-known experts in my field did it in this way. |
Mar
27 |
comment |
A lower-dimensional algebraic topology problem between homology group and fundamental group
@GabrielC.Drummond-Cole: could you please give me one such example? I tried, but still fails, the main problem for me is that I cannot make $\Omega$ a topological ball. Thanks. |
Mar
17 |
comment |
$H=W$ for weighted Sobolev spaces
@FanZheng As far as I know, the question is very hard. Even in the case $m=1$ and $\mu_0=\mu_1$, the essential known condition for the coincidence are the so-called $p$-admissible weight, where a kind of reverse H\"older's inequality is the key. |
Mar
3 |
comment |
Publication in proceedings
As far as I know, in mathematics, usually proceeding of a conference gives very high priority to the invited speakers and it is difficult to contribute in a proceeding. Many proceedingsar in celebration/memory of some well-known mathematicians or some bigger conferences will appear in MatheScinet as well. |
Mar
3 |
comment |
A lower-dimensional algebraic topology problem between homology group and fundamental group
@AlexDegtyarev: Thanks for reminder. Here $C\geq 1$ is an absolute constant. The interesting case is actually $C>1$. |