Functional analysis is the study of infinite-dimensional vector spaces, often with additional structures (inner product, norm, topology), with typical examples given by function spaces. The subject also includes the study of linear and non-linear operators on these spaces, as well as measure, ...

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Is the space of almost everywhere differentiable function with bounded derivative embedded with uniform norm complete?

Let $A$ be the space of almost everywhere differentiable functions $[0,1]\rightarrow [0,1]$, and when differentiable, their derivatives are bounded by $M$. I'm aware that the space of almost ...
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Prove or disprove that the following system $\left\{\frac{(-1)^{n-1}}{\pi}\left(\frac{\sin\pi t}{n-1-t}\right)\right\}_2^\infty$ is a Riesz basis.

Prove or disprove that the following system $$\left\{\frac{(-1)^{n-1}}{\pi}\left(\frac{\sin\pi t}{n-1-t}\right)\right\}_2^\infty$$ is a Riesz basis on $L^2(\mathbb R)$. I do not think it is a trivial ...