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 ...

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 …

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 …

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 …

Jul 8, 2019 · I am programming a basic mathematical library that deals with vectors, matrices, tensors, holors, functions, etc. I am wondering what the best terminology will be regarding …

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 …

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!

This is the common theme for Pointwise convergence problems and is why (in my opinion) we have this definition. To sum up: Uniform convergence is the intuitive definition.

Jul 29, 2021 · This proof involves rewriting the Fourier Series to its Dirichlet-kernel form, and the Riemann-Lebesgue Lemma is applied to prove pointwise convergence. A proof of the pointwise …

May 12, 2020 · Finding the Pointwise Limit of a Function Ask Question Asked 5 years, 6 months ago Modified 5 years, 6 months ago