All Questions

When we do Fourier analysis, we don't always get convergent series. A classic example comes from considering the Sawtooth function. It has Fourier Coefficients $$s(x) = \frac{1}{2} + \sum_{n \neq 0} \...

I'm thinking of the following question: Consider a function $f: U\rightarrow\mathbb{R}$ where $U=[0,L_1)\cup(L_1,L]$, and an energy functional $$F=\int_{U}\Big (\frac{\mathrm{d}f}{\mathrm{d}x}\Big)^2\...