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1d
comment notable inductive proofs relating to fractals
That paper showed what the spectrum is. Incidentally the proof for the spectrum actually can be used to also prove the limit Laplacian also exists. But that is an older result than this paper.
1d
comment notable inductive proofs relating to fractals
Fixed the links and added a longer description of what I was trying to say with the induction vs. iteration divide. Hope that helps.
1d
revised notable inductive proofs relating to fractals
added 363 characters in body
2d
answered notable inductive proofs relating to fractals
Feb
23
awarded  Necromancer
Feb
14
answered Can Hausdorff dimension make sets into a Tropical Semiring?
Dec
17
comment Modification of stochastic processes vs. generalized stochastic processes
It seems to me that the direct analogy of a modification to a generalized process would require a measure on $\mathcal{D}$ so you could talk about $\langle X,\varphi \rangle = \langle Y, \varphi \rangle$ for almost all $\varphi \in \mathcal{D}$. It is not clear to me that this interpretation would give anything particularly useful however. Or even be meaningful.
Dec
17
comment Is a semigroup always an exponential?
The answer to the first part of your question is to point you at the Hille-Yosida Theorem and its various cousins. They should be in any standard functional analysis textbook. More can't be said about the spectrum unless you have more detail about the operators $S(t)$.
Dec
5
awarded  Yearling
Nov
6
awarded  Nice Answer
Nov
6
answered Can this informal argument (for the fact that almost all reals in the unit interval are irrational) be saved?
Oct
14
awarded  Caucus
Jul
3
awarded  Civic Duty
Jun
14
answered How to define a differential form on a fractal?
May
21
comment Is there any result concerning on the metric dimension of inverse limit?
@Bingbing Liang, it is not clear to me right now whether the nonzero lower box counting dimension always holds for any compatible sequence of metrics. There are lots of metrics out there and I am not certain enough to rule out a counter example.
May
19
comment Is there any result concerning on the metric dimension of inverse limit?
@Misha thank you for making me think a bit longer about this. @Bingbing Liang yes, the idea is to do that and then take the limit. Z_2 is just the easiest example of this to write down.
May
19
revised Is there any result concerning on the metric dimension of inverse limit?
added 22 characters in body
May
19
answered Is there any result concerning on the metric dimension of inverse limit?
Apr
28
comment Mathematical properties of financial prices
@Stefan, the same objection could be used against any physical science. Yet, as a community, we do not give up hope of modeling in the face of other very complicated systems like particle physics or the global climate.
Apr
21
comment Sierpinski Triangle and the Chaos Game
If you choose some initial point $x_0$ and then applying some sequence of the three maps is equivalent to picking one of the points in the image of the IFS which by the Hausdorff convergence must approaching the Sierpinski gasket. So my original answer was not quite complete.