Variants of Parseval's Formula and the Grothendieck Inequality

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Constructs a Riesz products-based, explicit continuous injection from the l2 unit ball into L∞(Ω) that registers dot products by an integral, giving a Parseval-like formula and a constructive proof of the Grothendieck inequality. Uses Khinchin/Littlewood duality to produce uniformizing interpolants with L∞ bounds (Khinchin best constant √2) and an iterative correction whose error decays geometrically because the perturbation norm <1, so the series converges and the map is both norm- and weak-continuous.

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" chapters (13)

1. 0:00Representing Euclidean spaces
2. 3:33Harmonic analysis on cubes
3. 7:28The challenge of representation
4. 9:49Grothendieck's inequality
5. 14:02Dual statements and duality
6. 16:55Injectivity requirements
7. 20:05Khintchine inequality
8. 23:05Interpolation strategies
9. 26:30Iterative error correction
10. 30:27Uniformizing and continuity
11. 34:00Riesz products as a tool
12. 38:13Final theorem construction
13. 43:42Limitations and implications