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 …

Pointwise convergence means at every point the sequence of functions has its own speed of convergence (that can be very fast at some points and very very very very slow at others). Imagine …

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 · For the math term of projection Wikipedia links to "function composition", whose page in turn links to "pointwise". The question is: What is “pointwise”, in the context of function composition?

May 14, 2017 · $\left (2\right)$ What is the difference between boundedness, pointwise boundedness, and uniform boundedness? $\left (3\right)$ If my function is bounded for all $x$, does this imply that …

Feb 9, 2025 · It is a standard phnemenon: the pointwise convergence and uniform convergence do not coincide, even for sequences of linear operators.

Perhaps the problem is that you are only given a subsequence which converges almost everywhere, and there are uncountably many such sequences (so the total problem area where we don't …

Unfortunately my analysis lecturer, as awesome as he is, lacks the structure in his lessons to provide worked out proofs for us to use as guidelines for proving other things. Hence, I am having a g...

Apr 21, 2021 · 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!