bio | website | professor.ufabc.edu.br/… |
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location | Cotia, Brazil | |
age | 36 | |
visits | member for | 4 years, 8 months |
seen | 57 mins ago | |
stats | profile views | 1,021 |
I'm a professor at the Center of Mathematics, Computation and Cognition of the Federal University of the ABC, Santo André, Brazil.
Jul 12 |
revised |
Wave front set from the FBI or Segal-Bergman transform (and a motivation)
small typos corrected |
Jul 11 |
revised |
Wave front set from the FBI or Segal-Bergman transform (and a motivation)
Added explanation |
Jul 11 |
revised |
Wave front set from the FBI or Segal-Bergman transform (and a motivation)
Added explanation |
Jul 11 |
answered | Wave front set from the FBI or Segal-Bergman transform (and a motivation) |
Jun 17 |
revised |
Do locally convex topological vector spaces embed into diffeological spaces?
Added reference to complementary answer |
Jun 17 |
comment |
Exponential rule for Whitney-$\mathcal{C}^{\infty}$-topology
@JochenWengenroth or perhaps a "convenient-calculus" tag... |
Jun 17 |
comment |
Exponential rule for Whitney-$\mathcal{C}^{\infty}$-topology
@KathrinL. Igor's comment is still relevant. The graph topology on the space of continuous maps is the Whitney $C^0$ topology, and Peter Michor's argument works in the continuous case as well. |
Jun 16 |
comment |
Do locally convex topological vector spaces embed into diffeological spaces?
I have edited my answer to better suit your original question, based on your comments. I've also added a remark at the end concerning your remaining question, to which unfortunately I don't know an answer. Papers who cite Glöckner's work quoted above, according to MathSciNet, apparently don't even raise that question, let alone answer it. |
Jun 16 |
revised |
Do locally convex topological vector spaces embed into diffeological spaces?
Improved explanation in view of OP's comments, superfluous discussion on continuous linear maps removed |
Jun 15 |
comment |
Do locally convex topological vector spaces embed into diffeological spaces?
So, you were considering smooth maps (in either sense) as the arrows of the category of lctvs in your original question, and your residual question is whether the answer changes if you restrict the arrows to be smooth diffeomorphisms. Is this corrrect? |
Jun 15 |
revised |
Do locally convex topological vector spaces embed into diffeological spaces?
Improved explanation in view of comments by the OP |
Jun 15 |
revised |
Do locally convex topological vector spaces embed into diffeological spaces?
small rewording |
Jun 15 |
comment |
Do locally convex topological vector spaces embed into diffeological spaces?
@DavidRoberts so, what is the definition of "embedding of categories" you have in mind in your question? Do you put any restriction on the arrows in the category of lctvs besides being continuous linear maps (e.g. do you require them to be topological isomorphisms, or something)? |
Jun 15 |
revised |
Do locally convex topological vector spaces embed into diffeological spaces?
Conclusion rectified in order to match previously incompletely understood hypothesis, reasoning unchanged |
Jun 15 |
answered | Do locally convex topological vector spaces embed into diffeological spaces? |
Jun 6 |
comment |
constant rank theorem for banach spaces
Interesting. This means that the hypothesis that $M$ is finite-dimensional also removes the requirement that $\ker DF[u_0]$ should be a closed direct summand. That is very useful. Curiously, Glöckner's paper does not quote the book of Abraham et al. |
Jun 1 |
comment |
How can I calculate the adjoint of the wave operator $\square_{g}$ in $H^{k}$?
Notice, however, that you can use Stokes's theorem only if the boundary of the region is at least locally Lipschitz. |
Jun 1 |
comment |
How can I calculate the adjoint of the wave operator $\square_{g}$ in $H^{k}$?
I apologize, actually smooth functions / forms of compact support are dense only in $L^2$ for the region you specified. For $H^k$ you need to specify another dense domain - a possibility would be to choose smooth functions / forms in $H^k$ whose derivatives up to order $k$ extend continuously to the boundary, and then keep track of the boundary terms that appear due to Stokes's theorem. In this case, $\Box_g$ will no longer be symmetric in general due to those. Of course, this is only one choice of domain - the problem you are studying may impose another choice. |
Jun 1 |
comment |
How can I calculate the adjoint of the wave operator $\square_{g}$ in $H^{k}$?
It applies to both, since the domain of $\Box_g$ is assumed to be the (dense in both) linear subspace of smooth functions / forms with compact support. Again, $\Box_g$ is not defined as a linear operator from either Hilbert space into itself. |
May 31 |
comment |
How can I calculate the adjoint of the wave operator $\square_{g}$ in $H^{k}$?
By the way, what is your definition of $\mathcal{U}^+_t$? |