Related papers: Nevai's condition for measures with unbounded supp…

Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…

For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | \lambda_i - \lambda_j |^\beta \prod^n_{i=1} (2 - \lambda_i)^a (2 + \lambda_i)^b I_{(-2,2)} (\lambda_i) $$ $(a, b > -1, \beta > 0) $ a…

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…

We study the Dvoretzky covering problem for random covering sets driven by general Borel probability measures. As our main result, we solve the problem of covering analytic sets by random covering sets generated by arbitrary Borel…

We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is…

The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…

We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that for ergodic discrete Schrodinger…

In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-posedness of the Cauchy problem under $C^k$-regularity of…

The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit…

A unified framework is proposed for tests of unobserved heterogeneity in parametric statistic models based on Neyman's $C(\alpha)$ approach. Such tests are irregular in the sense that the first order derivative of the log likelihood with…

Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…

We study Widom factors for (a) monic orthogonal polynomials in $L^2$ with respect to the equilibrium measure of a compact set $K\subset\mathbb{R}$ and (b) residual polynomials normalized at an exterior point. Using weakly equilibrium Cantor…

We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential…

We prove the equivalence of ensembles for Bernoulli measures on $\mathbb{Z}$ conditioned on two conserved quantities under the situation that one of them is spatially inhomogeneous. For the proof, we extend the classical local limit theorem…

We prove a general existence theorem for nonlinear partial differential systems of any order in one complex variable. A special case of first order contains a well-known theorem of Nijenhuis and Woolf concerning local existence of…

This work extends Favard-type spectral representations for banded matrices $T$ beyond the bounded setting. It assumes that, for every $N\in\mathbb N_0$, there exists a shift $s_N\ge 0$ such that the shifted truncation $A_N:= T^{[N]}+s_N…

The paper considers a linear matrix inequality (LMI) that depends on a parameter varying in a compact topological space. It turns out that if a strict LMI continuously depends on a parameter and is feasible for any value of that parameter,…

Zernike polynomials are widely used in optics and ophthalmology due to their direct connection to classical optical aberrations. While orthogonal on the unit disk, their application to discrete data or non-circular domains--such as…

We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant…