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This paper begins a new approach to the $r$-trace formula, without removing the nontempered contribution to the spectral side. We first establish an invariant trace formula whose discrete spectral terms are weighted by automorphic…
We discuss approaches to computing eigenfunctions of the Ornstein--Uhlenbeck (OU) operator in more than two dimensions. While the spectrum of the OU operator and theoretical properties of its eigenfunctions have been well characterized in…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
In the article, some Huygens and Wilker type inequalities involving trigonometric and hyperbolic functions are refined and sharpened.
In this paper we study those polynomials orthogonal with respect to a particular weight over the union of disjoint intervals first introduced by N.I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This…
We study a particular type of Einstein warped-product manifold where the warping function must satisfy the homogeneous version of the screened Poisson equation. Under these assumptions, we show that the dimension of the manifold, the…
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…
In this paper we compute the third coefficient arising from the TYCZ-expansion of the epsilon function associated to a Kaehler-Einstein metric and discuss the consequences of its vanishing.
A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval $(0,1)$ is studied. This type of polynomials have direct applications in…
We study the geometry of functions from the plane to the plane. For a large special class we are able to count preimages and compute them. Both numerical and theoretical aspects are discussed. Some of the tools used are Whitney's…
We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean space via Gauss map. In this way, the result for Bernstein…
Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…
We discuss some basic properties of the Sibony functions and pseudometrics.
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces…
We study wide moments of Dirichlet $L$-functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Dirichlet $L$-functions (with arbitrary twists) extending results…
The twist-2 contributions to the polarized structure functions in deep inelastic lepton--hadron scattering are calculated including the exchange of weak bosons and using both the operator product expansion and the covariant parton model. A…
We compute the tree-level late-time graviton four-point correlation function, and the related quartic wavefunction coefficient, for Einstein gravity in de Sitter spacetime. We derive this result in several ways: by direct calculation, using…
M. E. Larsen evaluated the Wronskian determinant of functions $\{\sin(mx)\}_{1\le m \le n}$. We generalize this result and compute the Wronskian of $\{\sin(mx)\}_{1\le m \le n-1}\cup \{\sin((k+n)x\} $. We show that this determinant can be…