Related papers: On an extremal problem in two Siegel domains
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…
In this article new bounds for the convergence exponent of the two dimensional Tarry's problem are given.
We give sufficient conditions under which solutions of finite-difference schemes in the space variable for second order possibly degenerate parabolic and elliptic equations admit estimates of spatial derivatives up to any given order…
We describe a plan how to prove an effective Siegel theorem (about the exceptional Dirichlet character). We give a brief outline in Section 0. We give a more detailed plan in Sections 1-5. The missing details (mostly routine elementary…
This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…
The purpose of this paper is to calculate explicitly the volumes of Siegel sets which are coarse fundamental domains for the action of $\mathrm{SL}_n (\mathbb{Z})$ in $\mathrm{SL}_n (\mathbb{R})$, so that we can compare these volumes with…
In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equations and…
We consider the second best constant in the Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested with the existence of extremal functions for this inequality. This problem was tackled by Djadli-Druet [5] for…
A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral…
We find the exact upper estimate for the upper density of zeros of entire functions of exponential type whose indicator diagram is contained in a given interval.
In this work we describe a construction that leads to an explicit solution of the problem of differentiation of hyperelliptic functions. A classical genus $g=1$ example of such a solution is a result of F.G.Frobenius and L.Stickelberger.…
We establish upper bounds for the size of two-distance sets in Euclidean space and spherical two-distance sets. The main recipe for obtaining upper bounds is the spectral method. We construct Seidel matrices to encode the distance relations…
We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…
Let $K$ be an imaginary quadratic number field and let $L(s,\xi_{\ell})$ denote the Hecke $L$-function to an angular character $\xi_{\ell}$ with frequency $\ell$. We detect values of $\log |L(\tfrac12,\xi_{\ell})|$ with size at least…
We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases…
In a recent paper, Ng, Tang and Tsai (Math. Ann. 2020) have found an explicit formula for the squeezing function of an annulus via the Loewner differential equation. Their result has led them to conjecture a corresponding formula for planar…
In this paper, we derive a priori estimates for the gradient and second order derivatives of solutions to a class of Hessian type fully nonlinear parabolic equations with the first initial-boundary value problem on Riemannian manifolds.…
We develop approximations for the Riemann zeta function that enable high-precision computation within the critical strip and other vertical strips. These approximations combine the main sum of the Riemann-Siegel formula with a simple…
We obtain sharp estimates for the quasi norm of the maximal function of f when it satisfies certain conditions.