Cauchy problems and inverse problems in partial differential equations (PDEs) represent a class of challenging mathematical models where one seeks to determine unknown data inside a domain from ...
Also a few other equations related to this equation are often studied. (Equations which can be easily transformed to Cauchy functional equation or can be solved by using similar methods.) Is there some overview of basic facts about Cauchy equation and related functional equations - preferably available online?
I'm brushing up on some complex analysis basics. The following is a small question I have about the proof of Cauchy's Integral Formula in Conway's book "Functions of One Complex Variable".
My question is related with the definition of Cauchy sequence As we know that a sequence $(x_n)$ of real numbers is called Cauchy, if for every positive real number ε, there is a positive integer ...
How many proofs of the Cauchy-Schwarz inequality are there? Is there some kind of reference that lists all of these proofs?
I read in a research paper On Schwartz's C-spaces and Orlicz's O-spaces by S. Díaz Madrigal that if the sequence $(a_n)$ converges to zero and $(x_n)$ is a weakly unconditionally Cauchy sequence in a
If $ (x_n)$ is weakly unconditionally Cauchy in a Hausdorff locally ...
Cauchy-Schwarz inequality has been applied to various subjects such as probability theory. I wonder how to prove the following version of the Cauchy-Schwarz inequality for random variables: $$\...
Cauchy Criterion for Uniform Convergence of Functions Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
Such complicated examples! Here's a simple one: $\ {1/n}_ {n=1}^\infty$ is a Cauchy sequence in the interval $ (0,\infty)$ and does not converge within the interval $ (0,\infty)$ (with the usual metric). Of course you could tack $0$ onto the space and get $ [0,\infty)$, and within that larger space it converges. Every metric space has a completion, within which every Cauchy sequence converges.