Related papers: Gaussian Riemann Derivatives

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0,…

In this paper we consider the Stratonovich reflected stochastic differential equation $dX_t=\sigma(X_t)\circ dW_t+b(X_t)dt+dL_t$ in a bounded domain $\O$ which satisfies conditions, introduced by Lions and Sznitman, which are specified…

The most general change of variables theorem for the Riemann integral of functions of a single variable has been published in 1961 (by Kestelman). In this theorem, the substitution is made by an `indefinite integral', that is, by a function…

In this paper we prove that the Generalized Riemann Hypothesis (GRH) for functions in the class $\mathcal{S}^{\sharp\flat}$ containing the Selberg class is equivalent to a certain integral expression of the real part of the generalized Li…

In a recent paper, Belishev and Sharafutdinov consider a compact Riemannian manifold $M$ with boundary $\partial M$. They define a generalized Dirichlet to Neumann (DN) operator $\Lambda$ on all forms on the boundary and they prove that the…

The $k$th Dickson polynomial of the first kind, $D_k(x) \in {\mathbb Z}[x]$, is determined by the formula: $D_k(u+1/u) = u^k + 1/u^k$, where $k \ge 0$ and $u$ is an indeterminate. These polynomials are closely related to Chebyshev…

In this paper we give the absolutely new proof of a conjecture of R.F.Scott(1881) on the permanent of a Cauchy matrix $\ls \frac{1}{x_i-y_j} \rs_{1 \leqslant i,j \leqslant n},$ where $x_1, ..., x_n$ and $y_1, ..., y_n$ are the distinct…

A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally…

For any pair $(n,p)$, $n\in\mathbb{N}$ and $0<p<\infty$, it has been recently proved that a radial weight $\omega$ on the unit disc of the complex plane $\mathbb{D}$ satisfies the Littlewood-Paley equivalence $$…

This note reports partial results related to the Gaussian product inequality (GPI) conjecture for the joint distribution of traces of Wishart matrices. In particular, several GPI-related results from Wei (2014) and Liu et al. (2015) are…

The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy-Riemann…

Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…

Riemann's non-differentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also be given a…

The coinvariant algebra $R_n$ is a well-studied $\mathfrak{S}_n$-module that is a graded version of the regular representation of $\mathfrak{S}_n$. Using a straightening algorithm on monomials and the Garsia-Stanton basis, Adin, Brenti, and…

For the fundamental representations of the simple Lie algebras of type $B_{n}$, $C_{n}$ and $D_{n}$, we derive the braiding and fusion matrices from the generalized Yang-Yang function and prove that the corresponding knot invariants are…

We consider a fractional linear differential equation with successive derivatives given by $ \mathbb{D}_\alpha^{n}y+ p_{n-1}(x) \mathbb{D}_\alpha^{n-1}y+ \dots +p_{1}(x)\mathbb{D}_\alpha y+p_0(x)y=0$, where $\mathbb{D}_\alpha^{j}$ is the…

Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent…

In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some…

We establish an analogue of the first fundamental theorem of calculus for functions defined on the Wasserstein space of probability measures. Precisely, we show that if a function on the Wasserstein space is sufficiently regular in the…

Let $\mathcal{A}$ denote the class of analytic functions in the unit disk $\mathbb{D}$ of the form $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ and $\mathcal{S}$ denote the class of functions $f\in\mathcal{A}$ which are univalent ({\it i.e.},…