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Kernel density estimation via diffusion and the complex exponentials approximation problem
condensed density random matrices parabolic PDE
2012/6/21
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentica...
Commmuting exponentials in dimension at most 3
Matrix exponential Property L Rings and Algebras
2011/9/2
Abstract: Let A,B be two square complex matrices of dimension at most 3. We show that the following conditions are equivalent i) There exists a finite subset U included in {2,3,4,...} such that for ev...
The Feichtinger Conjecture for Exponentials
Beurling density fat Cantor set Feichtinger conjecture for exponentials
2011/2/24
The Feichtinger conjecture for exponentials asserts that the following property holds for every fat Cantor subset B of the circle group: the set of restrictions to B of exponential functions can be co...
A recursion identity for formal iterated logarithms and iterated exponentials
recursion identity formal iterated logarithms iterated exponentials
2011/1/18
We prove a recursive identity involving formal iterated logarithms and for-mal iterated exponentials. These iterated logarithms and exponentials appear in a nat-ural extension of the logarithmic forma...
Absolutely Representing Systems of Exponentials in the Spaces of Infinitely-Differentiable Functions and Extendability in the Sense of Whitney
Exponentials Infinitely-Differentiable Functions Extendability
2010/3/1
Let Q be a compactum in~\mathbb{R}p, p\geqslant1, such that int Q\neq\varnothing and Q=\overline{ int Q}. Denote by C\infty[Q] the space of functions from C\infty( int Q) uniformly continuous in int Q...
On a Problem of Mahler Concerning the Approximation of Exponentials and Logarithms
Mahler Concerning Approximation of Exponentials Logarithms
2010/11/1
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
Representing Systems of Exponentials and Projection on Initial Data in the Cauchy Problem
Cauchy Problem Exponentials Initial Data
2010/3/1
The Cauchy problem for the equation \begin{equation} Mw\equiv \sumj=0m\sums=0ljas,j\frac{\partials+jw(z1,z2)}{\partial z1s\partial z2j}=0 \end{equation} \begin{equation} \frac{\partialnw(z1,z2)}{\part...