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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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Bounding the discrete $l^p$ norm by the continuous $L^p$ norm for trigonometric polynomials
Let $ X_N = \text{span} \{\cos(2\pi lx): l=0, \cdots, N-1 \} $ with $ x \in [0, 1] $ and $ Y_N = \{v =(v_0, \cdots, v_{N-1}): v_j \in \mathbb{C}\} = \mathbb{C}^N $. Then $ X_N $ is the space of trigon …