We describe Salem’s proof of the Rademacher-Menshov Theorem, which shows that one constant works for all orthogonal expansions in all L2-spaces. By changing the emphasis in Salem’s proof we produce a lower bound for sums of vectors coming from bi-orthogonal sets of vectors in a Hilbert space. This inequality is applied to sums of columns of an invertible matrix and to Lebesgue constants.
|Name||Proceedings of the Centre for Mathematics and Its Applications, Australian National University|
|Publisher||Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University|
|Conference||CMA/AMSI Research Symposium (2006)|
|Period||21/02/06 → 24/02/06|
- orthogonal expansion
- Bessel’s inequality
- Lebesgue constants