We study the sine-kernel time--band limiting operator $S_c$ on $L^2(0,c)$ through the entropy-type trace $\operatorname{Tr}\varphi_u(S_c)$, where $\varphi_u(x)=\log(1+(e^u-1)x)-ux$. A Fourier factorization gives $S_c=A_c^*A_c$ and $\operatorname{Tr}S_c=c$. We derive an exact identity for $\operatorname{Tr}(S_c-S_c^2)$...
We prove explicit upper bounds for the number of eigenvalues of a one-dimensional time-frequency localization operator in an open transition window. An abstract residual-energy principle combines a rank-N approximant with the Hilbert-Schmidt energy of its remainder and retains the strict integer correction imposed by t...
Let $S_c=P_{(0,c)}QP_{(0,c)}$ be the one-dimensional sinc-kernel concentration operator, let $N_a(c)=\#{n:\lambda_n(c)>a}$, and set $\bar L=\log((1-\delta)/\delta)$. We prove, uniformly for each fixed $A>0$, the tail-side quantile formula $N_\delta(c)=c+\pi^{-2}\bar L\log(4\pi^2c/\bar L)+O_A(\log c+\bar L)$ for $6\le\b...
Let $S=P_{cA_0}Q_{B_0}P_{cA_0}$ be the spatio-spectral concentration operator of bounded sets $cA_0,B_0\subset\mathbb{R}^d$, and let $\Lambda_\varepsilon=\#\{n:\varepsilon<\lambda_n(S)<1-\varepsilon\}$ be its plunge count. For $A_0$ and $B_0$ finite disjoint unions of bounded axis-parallel open boxes, we prove an expli...
A. Azimifard· 1 citation
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
