A polynomial inequality (and some whining)
Arghhh!!! I have a meeting tomorrow with my advisor to discuss my progress in research over the past month or so, and I have nothing interesting to mention– partly because I haven’t spent as much time as I could have, but mostly just because I’m slow and dense. I just gave up on the two problems I’ve been looking at, since I’ve gotten nowhere on those, and am now reading his paper on the linear independence of spikes and sines so I can work on another idea he suggested. Namely, to adapt the technique used in the paper to get a bound on the expected spectral norm of a random rectangular submatrix of the Fourier matrix. I can’t get anything done on this tonight besides reading, but it looks interesting.
Question of the night: Let 
, show that the coefficients of the polynomial 
satisfy the inequality
It may help to look up Markov’s inequality for polynomials (bounding the derivatives of a polynomial in terms of the Chebyshev polynomials), and try to prove that.
Possibly relevant posts:
- Another basic spectral norm inequality (9/29/2008)
- Expected norm of matrices with randomly signed entries (8/6/2008)
- Research agenda (5/2/2008)