Related papers: The strong Haagerup inequality for q-circular syst…
The study of Khintchin inequalities has a long history in abstract harmonic analysis. While there is almost no possibility of non-trivial Khintchine inequality for central Fourier series on compact connected semisimple Lie groups, we…
In this paper, we prove the uniform estimates for the resolvent $(\Delta - \alpha)^{-1}$ as a map from $L^q$ to $L^{q'}$ on real hyperbolic space $\mathbb{H}^n$ where $\alpha \in \mathbb{C}\setminus [(n - 1)^2/4, \infty)$ and $2n/(n + 2)…
We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every $ (1+ \varepsilon)$-quasi-isometry of the John domain of the Heisenberg group $ \mathbb {H} $ is close to some isometry with…
We investigate a Riemann-Hilbert problem (RHP), whose solution corresponds to a group of $q$-orthogonal polynomials studied earlier by Ismail et al. Using RHP theory we determine new asymptotic results in the limit as the degree of the…
We build on the results of [6] to show that the homology groups $\mathrm{H}_{r_1+r_2}(Y_0(\mathcal{N}_\Sigma),\mathcal{O})_{\mathfrak{m}_\Sigma}$ of arithmetic manifolds are free over certain deformation rings $R_\Sigma$, when there are…
We consider a class of multiparameter singular Radon integral operators on the Heisenberg group ${\mathbb H}^1$ where the underlying variety is the graph of a polynomial. A remarkable difference with the euclidean case, where Heisenberg…
Let $I$ be a homogeneous ideal in the polynomial ring $R = k[z_1, \cdots, z_n]$ , where $k$ is an algebraically closed field of characteristic zero. Macaulay's Theorem provides constraints on the Hilbert function of $I$ or $R/I$ from one…
For the class of quantum integrable models generated from the $q-$Onsager algebra, a basis of bispectral multivariable $q-$orthogonal polynomials is exhibited. In a first part, it is shown that the multivariable Askey-Wilson polynomials…
We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant for those elements whose Gibbs state is zero. The main ingredient of our proof is…
We show that if a compact, connected, and oriented $n$-manifold $M$ without boundary admits a non-constant non-injective uniformly quasiregular self-map, then the dimension of the real singular cohomology ring $H^*(M; \mathbb{R})$ of $M$ is…
The hypercontractivity inequality for the qubit depolarizing channel $\Psi_t$ states that $\|\Psi_t^{\otimes n}(X)\|_p\leq \|X\|_q$ provided that $p\geq q> 1$ and $t\geq \ln \sqrt{\frac{p-1}{q-1}}$. In this paper we present an improvement…
We study Hamiltonicity in random subgraphs of the hypercube $\mathcal{Q}^n$. Our first main theorem is an optimal hitting time result. Consider the random process which includes the edges of $\mathcal{Q}^n$ according to a uniformly chosen…
For a Weyl group W and its reflection representation mathfrak{h}, we find the character and Hilbert series for a quotient ring of C[mathfrak{h} oplus mathfrak{h}^*] by an ideal containing the W--invariant polynomials without constant term.…
We study the Fourier coefficients of functions satisfying a certain version of Wright's circle method with finitely many major arcs. We show that the Jensen polynomials associated with such Fourier coefficients are asymptotically…
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal…
We study a new family of q-Meixner multiple orthogonal polynomials of the first kind. The discrete orthogonality conditions are considered over a non-uniform lattice with respect to different q-analogues of Pascal distributions. We address…
We use Kor\'anyi--Reimann complex cross--ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of complex hyperbolic space and the first Heisenberg group.
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed…
In this article we obtain an "off-diagonal" version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12]…
We prove uniform ``pseudo-Siegel'' a priori bounds for Siegel disks of bounded type that give a uniform control of oscillations of their boundaries in all scales. As a consequence, we construct the Mother Hedgehog controlling the…