3,588 reputation
12051
bio website regularize.wordpress.com
location Braunschweig, Germany
age 37
visits member for 4 years, 11 months
seen 14 hours ago

Professor at TU Braunschweig.

Area: Inverse problems, regularization theory, applied functional analysis, mathematical image processing.


Aug
29
comment Convergence of Fixed-Point Iteration of a dependent map
Have you looked at the properties of the corresponding iteration the product space?
Aug
24
comment Hyperfunctions supported at a point
Ha! Page 5 is not available in google books for me, this explains my ignorance…
Aug
24
comment Hyperfunctions supported at a point
I don't know much about hyperfunctions but I am not sure what "coincide" should mean here. A distribution is an element in the dual of smooth functions with compact support while a hyperfunction is an equivalence class of holomorphic functionals. I do not see a canonical way to map one set into the other… E.g. how should a hyperfunction act on a smooth function and how to make such an identification that respects all wanted rules (such as the rules for the derivative…)?
Aug
22
comment Construct a PDE solution from a net of approximations
@AlexM. I guess that your limit is something like "largest set in the partition goes to zero". Why not pick sequences of such converging partitions and show that limits are independent of the subsequences?
Aug
22
comment Construct a PDE solution from a net of approximations
@IgorKhavkine This counterexample does not work with unique solutions (as requested by the OP or the edited question with explicit boundary conditions).
Aug
22
comment Identities and inequalities in analysis and probability
This is not widely known?
Aug
22
comment Construct a PDE solution from a net of approximations
@IgorKhavkine I guess the difference is that the OP does not assume that $x_i$ converges to $x$ but only that $f(x)$ converges to zero and wants to conclude the convergence of the $x_i$.
Aug
22
comment Construct a PDE solution from a net of approximations
I can't imagine a situation in which one naturally has a net of a solution of a PDE which is not a sequence. But maybe that's only my limited imagination…
Aug
16
comment Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
In convex analysis the term indicator functions is used for a function that is zero in some set and plus infinity elsewhere.
Aug
9
comment Do convolution and multiplication satisfy any nontrivial algebraic identities?
For the anonymous user: You misunderstood the (abused ) notation. The product there is the tensor product and not the point wise product.
Jul
24
comment How to calculate $det(X^TX)$ efficiently, update one column of X each time
Not a good fit for this side - I suggest scicomp.stackexchange.com. Anyway: Why not do a factorization of $X_1$ (LU or QR) and down- and update that?
Jul
24
comment 9-point stencil “equivalent” for advection equation
This question should go well on scicomp.stackexchange.com.
Jul
17
comment question about $TGV^2$ space
Added something on the interpretation with Radon measures…
Jul
17
comment Is this has anything to do with Riesz representation?
Nope, not linear since flipping the sign of my won't flip the sign of the value.
Jul
17
comment Is this has anything to do with Riesz representation?
One more thing: Your functional is not linear but only positively homogeneous, so what kind of result do you expect?
Jul
17
comment Is this has anything to do with Riesz representation?
What form of Sobolev norm are you using, i. e. how are the sup-norm of the function and it's derivative combined?
May
20
comment Projecting a convex partition onto a convex set
Err, sorry - of course, nonempty $X$ it should be…
May
20
comment Projecting a convex partition onto a convex set
$X$ could be empty or have $n-1$ points... You need some more conditions.
May
19
comment Splines linearly independent
What do you mean by "its unique smooth extension"?
May
14
comment Which way for reading the proofs?
@fanzheng I heard a similar quote about a famous optimizer "I don't read papers, I write them."