A mini-max problem for self-adjoint Toeplitz matrices

Details A mini-max problem for self-adjoint Toeplitz matrices A mini-max problem for self-adjoint Toeplitz matrices

2010-09-14

arxiv.org/abs/1009.2553v2

Mathematics

Functional Analysis

14 pages, new references added, typos fixed

Scientific paper

We study a minimum problem and associated maximum problem for finite, complex, self-adjoint Toeplitz matrices. If $A$ is such a matrix, of size $(N+1)$-by-$(N+1)$, we identify $A$ with the operator it represents on $P_N$, the space of complex polynomials of degrees at most $N$, with the usual Hilbert space structure it inherits as a subspace of $L^2$ of the unit circle. The operator $A$ is the compression to $P_N$ of the multiplication operator on $L^2$ induced by any function in $L^{\infty}$ whose Fourier coefficients of indices between $-N$ and $N$ match the matrix entries of $A$. Our minimum problem is to minimize the $L^{\infty}$ norm of such inducers. We show there is a unique one of minimum norm, and we describe it. The associated maximum problem asks for the maximum of the ratio of the preceding minimum to the operator norm. That problem remains largely open. We present some suggestive numerical evidence.

Affiliated with

Also associated with

No associations

Rating

A mini-max problem for self-adjoint Toeplitz matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A mini-max problem for self-adjoint Toeplitz matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A mini-max problem for self-adjoint Toeplitz matrices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-394754