Is there a notation for element-wise (or pointwise) operations? For example, take the element-wise product of two vectors x and y (in Matlab, x .* y, in numpy x*y), producing a new vector of same ...

Jul 8, 2019 · When talking vectors/matrices/tensors, pointwise is best avoided because it is decently ambiguous, since vectors can be interpreted as points. So a pointwise multiplication might just be …

The pointwise convergence depends on each x x, that is you need to count and fix every x x before passing to the limit. On the other hand, uniform convergence is independent of x x.

The second one is uniform continuity, ive just forgot to change the name (because i copied and modified from the pointwise version). Thanks anyway.

Sep 25, 2015 · Similarly, you could say that vector addition is 'pointwise addition' because you're adding the entries in parallel according to their indices. In the article, rather, it is just using it to mean that …

Feb 9, 2025 · For pointwise convergence everywhere, x x is picked first, then an N N is found which works for that x x. Different values of x x can have different N N. With convergence in the operator …

Oct 3, 2020 · Sequence of continuous functions on $ [0,1]$ pointwise converging to an unbounded function Ask Question Asked 5 years, 3 months ago Modified 2 years, 3 months ago

Apr 21, 2021 · Commented Apr 28, 2012 at 14:10 1 Choosing suitable intervals with length going to zero you can exhibit a sequence of L^p, but pointwise the sequence doesn't converges at any point!

Jul 25, 2021 · Intuitively I feel like that weak convergence only controls the behavior of integral (by Riesz Representation Theorem), which cannot affect pointwise structure. But I don't know how to construct …

Everywhere pointwise convergence is necessary to guarantee that fn → f f n → f pointwise if every subsequence has a further subsequence which converges to f f pointwise. With that being said, this …