Questions tagged [real-analysis]

For questions about real analysis, a branch of mathematics dealing with limits, convergence of sequences, construction of the real numbers, least upper bound property and related analysis topics, such as continuity, differentiation, and integration through the Fundamental Theorem of Calculus.

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+100

proving that $\frac{d}{dx}\phi_j(x)=\frac{4}{l}\sum_{m=0 \\ (j+m) odd}^{j-1}\frac{3j-2m}{\xi_m}\phi_m(x)+\eta^l_j(x)$

Given that $$\frac{d}{dx}T^l_k(x)=\frac{1}{l}\sum_{m=0 \\(k+m)odd}^{k-1}\frac{4k} {\xi_m}T^l_m(x)$$ AND $$\phi_j(x)=x(l-x)T^l_j(x)$$ Where $$ \xi_m = \left\{ \begin{array}{ll} 2 & m = 0 \\ ...
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+50

Is the space of maps which satisfy this vanishing condition finite-dimensional?

Let $\mathbb{D}^n \subseteq \mathbb{R}^n$ be the closed $n$-dimensional unit ball. Let $h:\mathbb{D}^n \to \mathbb{R}^{k}$ be smooth, and suppose that $h(x) \neq 0$ a.e. on $\mathbb{D}^n$. Set $$V_h=\...