arXiv subjects

Ahmadreza Azimifard

Publications and source records attributed to Ahmadreza Azimifard.

11 recordsLinked to original sources

arXiv2026

Componentwise and Measure-Sensitive Bounds for One-Dimensional Time-Frequency Localization

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 the open threshold. For the Fourier kernel, centered least-squares polynomials, optimized moments, and Chebyshev-Bessel truncations improve or match the diameter-Taylor certificate; on interval blocks the moment envelope gains the exact factor 1/(2N+1). Finite measurable partitions yield best-polynomial matrix and residual-energy bounds, together with two-level threshold allocations that exploit spatial or Fourier-side orthogonality and remain stable under large empty gaps. A complementary defect channel gives a componentwise variational Schatten envelope for finite interval unions. For arbitrary finite-measure hard windows, exact cross-boundary and symmetric-difference formulas give strict transition counting and a certified near-one cluster that can be subtracted from direct counts. We also treat integrable soft masks, a root-sum-square core-tail decomposition, and unbounded windows controlled by moments. An explicit unbounded finite-measure set has all polynomial moments and infinite fractional translation perimeter for every order in (0,1], yet admits an O(log(1/epsilon)/log log(1/epsilon)) certificate. Finally, kernels with finitely many bounded separated phase interactions and finite separated amplitude rank admit factorial, least-squares, Chebyshev-Bessel, span-compressed, and anisotropic-degree bounds. For bounded hard Fourier windows, the final hybrid is no larger than the corresponding earlier certificates proved here; no universal comparison with all regular-domain estimates is asserted.

math.FA↗

arXiv2026

Scale-free Hankel factorization and explicit one-dimensional plunge bounds for time-frequency localization operators

The plunge region records the spectral transition of a time-frequency localization operator. Let $A_0,B_0\subset\mathbb{R}$ be bounded measurable sets of positive measure with finite boundaries, and let $S_{cA_0,B_0}=P_{cA_0}Q_{B_0}P_{cA_0}$. We prove that, for every $c>0$ and $0<\varepsilon<1/2$, $Λ_\varepsilon\le C(A_0,B_0)\widetilde L[1+\ln_+(ca/\widetilde L)]$, where $\widetilde L=\ln(1/[\varepsilon(1-\varepsilon)])$, and $\ln_+x=\max(0,\ln x)$. If $M$ and $K$ count the interval components and $a$ and $b$ are their maximal lengths, one may take $C(A_0,B_0)=63MK(1+b)$. The estimate is uniform in $c$ and $\varepsilon$ and becomes $O(\widetilde L)$ when $\widetilde L\ge ca$. On the range $c\ge2$ and $α^{-c}<\varepsilon<1/2$ covered by the parallelepiped theorem of Kulikov and Dam Larsen (2026), this recovers its $d=1$ order; their complementary very-small-threshold result is sharper. We give an independent direct proof with explicit geometry dependence and a single formulation for all $c$ and $\varepsilon$. It acts on the off-diagonal factor of the localization operator: an exact one-dimensional oscillation factorization reduces each far-field piece to two modulated copies of the scale-free Hankel kernel $1/[2π(s+r)]$, Bernstein-ellipse approximation gives uniform singular-value decay, and a Taylor-rank estimate controls the boundary layer. Choosing this width at the spectral depth absorbs finer scales and leaves only $\ln_+(ca/\widetilde L)$ dyadic scales, yielding the self-improving logarithm. It also identifies tangential phase dependence as an obstruction to this factorization in nonproduct higher-dimensional geometry.

math.FA↗

arXiv2026

Uniform sine-kernel determinant asymptotics, tail-side quantiles, and prolate eigenvalue bounds

Let $S_c=P_{(0,c)}QP_{(0,c)}$ be the one-dimensional sinc-kernel concentration operator, let $N_a(c)=\#{n:λ_n(c)>a}$, and set $\bar L=\log((1-δ)/δ)$. We prove, uniformly for each fixed $A>0$, the tail-side quantile formula $N_δ(c)=c+π^{-2}\bar L\log(4π^2c/\bar L)+O_A(\log c+\bar L)$ for $6\le\bar L\le A\log c$. It yields corresponding additive formulas for the lower half and full plunge, with main terms respectively $π^{-2}\bar L\log(4π^2c/\bar L)$ and twice this quantity. An exact one-tail-coordinate selection gives, for fixed $A>0$, $d\ge1$, and $q\in(1/2,1)$, the one-sided tensor-product bound $Λ_δ(c;d)\geπ^{-2}d c^{d-1}\bar L\log(4π^2c/\bar L)-O_{A,d,q}(c^{d-1}(\log c+\bar L))$ for $L_{d,q}\le\bar L\le A\log c$, where $L_{d,q}=\log(q^{-(d-1)}(e^6+1)-1)$; the tensor content is nontrivial for $d\ge2$. The analytic input is a signed growing-parameter sine-kernel determinant asymptotic: uniformly for $0\leω\le A\log s$, $\log\det(I+(e^{2ω}-1)K_s)=4ωs/π+2π^{-2}ω^2\log(4s)+2\log|G(1+iω/π)|^2+O_A((1+ω)^4\log^2s/s)$, where $G$ is the Barnes $G$-function. We prove this negative-coupling counterpart of the Bothner--Deift--Its--Krasovsky theorem by direct IIKS steepest descent. We also retain the uniform head-side results and use a two-way determinant reduction to obtain the moving-depth lower-half bridge bound with constant $1/(32π^2)$; extending it to the deeper range uses Kulikov--Dam Larsen and may require a smaller constant. These counting formulas are additive. Their errors become uniformly relative when $\bar L$ tends uniformly to infinity; fixed thresholds are covered separately by Landau--Widom. A Lambert-$W_{-1}$ formula is recorded only for the continuous main term, not for individual eigenvalues.

math.FA↗

arXiv2026

Entropy-type traces and moment expansions for the sine-kernel time-band limiting operator

We study the sine-kernel time--band limiting operator $S_c$ on $L^2(0,c)$ through the entropy-type trace $\operatorname{Tr}φ_u(S_c)$, where $φ_u(x)=\log(1+(e^u-1)x)-ux$. A Fourier factorization gives $S_c=A_c^*A_c$ and $\operatorname{Tr}S_c=c$. We derive an exact identity for $\operatorname{Tr}(S_c-S_c^2)$ and the lower bound $\operatorname{Tr}(S_c-S_c^2)\geπ^{-2}\log c-π^{-3}$, which in turn yields $\operatorname{Tr}φ_u(S_c)\ge u\log c/(4π^2)$. We also obtain a positive moment expansion $\operatorname{Tr}φ_u(S_c)=\sum_{n\ge1}A_n(u)T_n(c)$ and, for each fixed $n$, the Landau--Widom asymptotic $T_n(c)=\log c/(π^2n)+o_n(\log c)$. Three natural uniformity hypotheses, denoted (LC), (MT), and (QM), lead to a quadratic lower bound of order $u^2\log c$ on logarithmically growing windows. We prove the implications among these hypotheses and the resulting bounds, with explicit constants, and explain why the fixed-index asymptotic alone does not provide the required uniformity. The hypotheses themselves remain open. Finally, a signed growing-parameter sine-kernel determinant theorem from a companion paper gives the quadratic lower bound independently of (LC), (MT), and (QM). This separates the conclusions available from elementary operator methods from those that use Riemann--Hilbert asymptotics.

math.FA↗

arXiv2026

Tensor factorization and explicit spectral bounds for product-box concentration operators

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 $Λ_\varepsilon=\#\{n:\varepsilon<λ_n(S)<1-\varepsilon\}$ be its plunge count. For $A_0$ and $B_0$ finite disjoint unions of bounded axis-parallel open boxes, we prove an explicit uniform upper bound on $Λ_\varepsilon$, valid for every $d\geq1$, $c>0$, and $0<\varepsilon<1/2$, with all constants written in terms of the side lengths. On the range $α\geq4$, $c\geq2$, and $α^{-c}<\varepsilon<1/2$, it gives $Λ_\varepsilon\leq Cc^{d-1}\log(1/\varepsilon)\log\!\bigl(αc/\log(1/\varepsilon)\bigr)$. Kulikov and Dam Larsen previously proved this order on that range for a broader class; the present contribution is an independent proof and an explicit all-parameter estimate for product boxes. The proof uses a telescoping tensorization of $P_{(cA_0)^c}Q_{B_0}P_{cA_0}$ into $d$ elementary tensor operators, with one one-dimensional off-diagonal factor and $d-1$ localization factors. Schatten quasi-norms then multiply across tensor factors, and the single logarithm arises only from the normal direction. For the model cube pair, we also prove that, when $\varepsilon<4^{-d}$, $Λ_\varepsilon\geq M_a^d=Ω((\log c)^d)$. Using an exact trace identity, an explicit cubic minorant, and the sine-kernel determinant asymptotics of Basor and Widom, we further obtain $\operatorname{Tr}((S-S^2)^m)=β_mπ^{-2}\log c+O_m(1)$ for each fixed $m$, where $β_m=B(m,m)$, together with a two-sided fixed-depth window estimate of order $\log c$. The lower bound is not matching, and the fixed-order statements are not uniform in $m$.

math.FA↗

arXiv2009

On the Amenability of Compact and Discrete Hypergroup Algebras

Let $K$ be a commutative compact hypergroup and $L^1(K)$ the hypergroup algebra. We show that $L^1(K)$ is amenable if and only if $π_K$, the Plancherel weight on the dual space $\widehat{K}$, is bounded. Furthermore, we show that if $K$ is an infinite discrete hypergroup and there exists $α\in \widehat{K}$ which vanishes at infinity, then $L^1(K)$ is not amenable. In particular, $L^1(K)$ fails to be even $α$-left amenable if $π_K(\{α\})=0$.

math.FA↗

arXiv2009

α-Amenable Hypergroups

Let $K$ denote a locally compact commutative hypergroup, $L^1(K)$ the hypergroup algebra, and $α$ a real-valued hermitian character of $K$. We show that $K$ is $α$-amenable if and only if $L^1(K)$ is $α$-left amenable. We also consider the $α$-amenability of hypergroup joins and polynomial hypergroups in several variables as well as a single variable.

math.FA↗

arXiv2008

On Character Amenability of Banach Algebras

Associated to a nonzero homomorphism $φ$ of a Banach algebra $A$, we regard special functionals, say $m_φ$, on certain subspaces of $A^\ast$ which provide equivalent statements to the existence of a bounded right approximate identity in the corresponding maximal ideal in $A$. For instance, applying a fixed point theorem yields an equivalent statement to the existence of a $m_φ$ on $A^\ast$; and, in addition we expatiate the case that if a functional $m_φ$ is unique, then $m_φ$ belongs to the topological center of the bidual algebra $A^{\ast\ast}$. An example of a function algebra, surprisingly, contradicts a conjecture that a Banach algebra $A$ is amenable if $A$ is $φ$-amenable in every character $φ$ and if functionals $m_φ$ associated to the characters $φ$ are uniformly bounded. Aforementioned are also elaborated on the direct sum of two given Banach algebras.

math.FA↗

arXiv2008

Amenability properties of the centres of group algebras

Let G be a locally compact group, and ZL1(G) be the centre of its group algebra. We show that when $G$ is compact ZL1(G) is not amenable when G is either nonabelian and connected, or is a product of infinitely many finite nonabelian groups. We also, study, for some non-compact groups G, some conditions which imply amenability and hyper-Tauberian property, for ZL1(G).

math.FA↗

arXiv2008

On the alpha-Amenability of Hypergroups

Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $α$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also shown that a Sturm-Liouville hypergroup with a positive index is $α$-amenable if and only if $α=1$.

math.FA↗

arXiv2008

Hypergroups with Unique Alpha-Means

Let $K$ be a commutative hypergroup and $α\in \hat{K}$. We show that $K$ is $α$-amenable with the unique $α$-mean $m_α$ if and only if $m_α\in L^1(K)\cap L^2(K)$ and $α$ is isolated in $\hat{K}$. In contrast to the case of amenable noncompact locally compact groups, examples of polynomial hypergroups with unique $α$-means ($α\not=1$) are given. Further examples emphasize that the $α$-amenability of hypergroups depends heavily on the asymptotic behavior of Haar measures and characters.

math.GR↗