For every q>2, the paper shows M_q is at most the integral of a power of the derivative of the optimal concentration function, and this bound is asymptotically sharp: M_q ~ sqrt(6/(pi q)) as q tends to infinity.
Optimal concentration in the Paley-Wiener space
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
Let $\Omega \subset \mathbb{R}$ be a bounded interval and let $PW(\Omega )$ be the corresponding Paley--Wiener space. For a measurable set $E\subset \mathbb{R}$ of finite measure, consider the largest possible fraction of the $L^{2}$-mass of a function in $PW(\Omega )$ that can lie in $E$. We prove that this concentration is no larger than the concentration attained on an interval of measure $\lvert E\rvert $. Thus, \emph{intervals optimize concentration in the Paley-Wiener space of band-limited functions.} The proof, based on an universality-type limit of the reproducing kernel of analytic trigonometric polynomials on the circle, has two steps. First, we establish an \emph{optimal concentration theorem for analytic trigonometric polynomials on the circle}. Second, the universality-type limit transfers the result from the circle to the real line, by controlling the expansion of circles whose projection kernels are midpoint Riemann sums for the Paley--Wiener sinc kernel.
citation-role summary
background 2
citation-polarity summary
years
2026 3roles
background 2polarities
unclear 2representative citing papers
The passive rearrangement of a density operator maximizes convex Husimi functionals and minimizes Wehrl entropy among states with the same spectrum, and spherical caps maximize all Ky Fan sums of Toeplitz operators on the sphere.
For every k and every prescribed measure, the supremum of the sum of the first k Toeplitz eigenvalues is attained, in the Fock space and in a general wavelet setting.
citing papers explorer
-
A Note on the Norm of the Embedding of $\text{PW}^2$ into $\text{PW}^q$
For every q>2, the paper shows M_q is at most the integral of a power of the derivative of the optimal concentration function, and this bound is asymptotically sharp: M_q ~ sqrt(6/(pi q)) as q tends to infinity.
-
Isospectral majorization and isoperimetric inequalities for coherent states on the Bloch sphere
The passive rearrangement of a density operator maximizes convex Husimi functionals and minimizes Wehrl entropy among states with the same spectrum, and spherical caps maximize all Ky Fan sums of Toeplitz operators on the sphere.
-
On the existence of extremizers for the sum of eigenvalues of Toeplitz operators
For every k and every prescribed measure, the supremum of the sum of the first k Toeplitz eigenvalues is attained, in the Fock space and in a general wavelet setting.