by Anthony Salib | Oct 7, 2020 | Uncategorized

Nothing works anymore 🙁 Problems attached! Problem4Download
by Anthony Salib | Sep 30, 2020 | Problem Solving, Pure Maths

So this problem comes from the functional analysis course I took last semester. Although simple, I thought was pretty cool. In the actual exercise they had broken it down into three parts, which I did not show in the problem post. Here I will show the steps as claims....
by Anthony Salib | Sep 24, 2020 | Pure Maths

So guess what happened again, another WordPress malfunction… something really isn’t right here. The blog post is attached! Open Mapping BlogDownload
by Anthony Salib | Sep 22, 2020 | Problem Solving, Pure Maths

Supposed that $u, f\in L^2(\Omega)$ satisfies $$\int_{\Omega}u\Delta^2 \phi^2 = \int_{\Omega} f\phi dx,$$ for all $\phi \in A = \{u\in H^4\cap H^1_0 (\Omega) : ~\Delta u \in H^1_0(\Omega)\}$. Prove that $u\in A$.
by Anthony Salib | Sep 22, 2020 | Problem Solving, Pure Maths

So once again, WordPress doesn’t like my Latex, so I have attached this blog as a pdf. Enjoy! PrbWk2Download
by Anthony Salib | Sep 2, 2020 | Uncategorized

So for some reason my usual way of writing Latex on the blog doesn’t work for this post. I have no idea why unfortunately, so I will just add the post as a PDF attached to this! Solution to Problem 1Download
by Anthony Salib | Aug 23, 2020 | Uncategorized

So last week we talked about the Baire Category Theorem, and this important tool will give us three equivalent theorems about the qualitative properties of operators on Banach spaces. Today we will begin with the first theorem, uniform boundedness. The proof of this...
by Anthony Salib | Aug 23, 2020 | Problem Solving, Pure Maths

This one is simple! Why is $L^{\infty}(\Omega)$ called ell-infinity?
by Anthony Salib | Aug 16, 2020 | Problem Solving

So this problem is in line with the post of this week, Baire’s Lemma. Have a go and let me know your thoughts in the comments! Let $D\subset (0,\infty)$ be unbounded and open. Then let the set $$G=\{x\in (0,\infty); nx\in D ~\text{for infinitely...
by Anthony Salib | Aug 13, 2020 | Uncategorized

So today I am starting a new series on the Principles of Functional Analysis to give you all an appreciation for the power that these simple truths hold. We will start today with Baire’s Lemma , which will require some definitions, hopefully, all familiar. (If...
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