相关论文: Bloch functions and asymptotic tail variance
We prove that the Bergman kernel function associated to a smooth measure supported on a piecewise-smooth maximally totally real submanifold K in C^n is of polynomial growth (e.g, in dimension one, K is a finite union of transverse Jordan…
In this paper we prove an analogue of the discrete spherical maximal theorem of Magyar, Stein, and Wainger, an analogue which concerns maximal functions associated to homogenous algebraic surfaces. Let $\mathfrak{p}$ be a homogenous…
We explore the information geometry and asymptotic behaviour of estimators for Kronecker-structured covariances, in both growing-$n$ and growing-$p$ scenarios, with a focus towards examining the quadratic form or partial trace estimator…
BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine functions. In particular, this approximation is area-strictly…
The paper continues the author's research in the problem of quantitative investigation of basic curvelinear quasiinvariants of quasiconformal curves. It concerns polygons with infinite number of vertices and provides various distortion…
The classical theorem of Bloch (1924) asserts that if $f$ is a holomorphic function on a region that contains the closed unit disk $|z|\leq 1$ such that $f(0) = 0$ and $|f'(0)| = 1$, then the image domain contains discs of radius…
The P\"ochl-Teller effective potential mimics an asymptotically de Sitter black hole bounded by an event horizon and a cosmological one. Owing to the benefit of being analytically soluble, the asymptotic quasinormal modes in the modified…
We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…
We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Talagrand by giving a one-term asymptotic expansion for large…
It has been shown recently that deformations of some integrable field theories in (1+1)-dimensions possess an infinite number of charges that are asymptotically conserved in the scattering of soliton like solutions. Such charges are not…
We consider a magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a two-dimensional Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the…
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros is extended to subharmonic functions in $\mathbb{R}^n, n\geq 3$. We also show that the existence of the limit $\lim_{\rti} \frac{\log…
We consider two classes of piecewise expanding maps $T$ of $[0,1]$: a class of uniformly expanding maps for which the Perron-Frobenius operator has a spectral gap in the space of bounded variation functions, and a class of expanding maps…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
We prove a new off-diagonal asymptotic of the Bergman kernels associated to tensor powers of a positive line bundle on a compact K\"ahler manifold. We show that if the K\"ahler potential is real analytic, then the Bergman kernel accepts a…
We derive asymptotic estimates for the growth of the norm of the deformed Hankel transform on the deformed Hankel--Lipschitz space defined via a generalised modulus of continuity. The established results are similar in nature to the…
We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of $L^p$ with $p<1$. We also obtain counterexamples that are asymptotically optimal with our positive…
For a closed smooth manifold $M$ admitting a symplectic structure, we define a smooth topological invariant $Z(M)$ using almost-K\"ahler metrics, i.e. Riemannian metrics compatible with symplectic structures. We also introduce $Z(M,…
In this thesis, the tail properties of multivariate Archimedean copulas are investigated using known representation theorems involving L1-norm symmetric distributions and the Williamson d-transform. Several new results on the asymptotic…
Suppose that a polarised K\"ahler manifold $(X,L)$ admits an extremal metric $\omega$. We prove that there exists a sequence of K\"ahler metrics $\{ \omega_k \}_k$, converging to $\omega$ as $k \to \infty$, each of which satisfies the…