Zobrazeno 1 - 10
of 78
pro vyhledávání: '"Goldman, Gil A."'
Autor:
Goldman, Gil, Yomdin, Yosef
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} |f(z)|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty interior, then for
Externí odkaz:
http://arxiv.org/abs/2402.01388
Autor:
Goldman, Gil, Yomdin, Yosef
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \| f(z) \|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty interior, then
Externí odkaz:
http://arxiv.org/abs/2309.03975
Autor:
Goldman, Gil, Yomdin, Yosef
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \|f(z)\|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty interior, then fo
Externí odkaz:
http://arxiv.org/abs/2308.14722
Autor:
Batenkov, Dmitry, Goldman, Gil
Following recent interest by the community, the scaling of the minimal singular value of a Vandermonde matrix with nodes forming clusters on the length scale of Rayleigh distance on the complex unit circle is studied. Using approximation theoretic pr
Externí odkaz:
http://arxiv.org/abs/2107.09326
Let $f(z) = \sum_{k=0}^\infty a_k z^k$ be an analytic function in a disk $D_R$ of radius $R>0$, and assume that $f$ is $p$-valent in $D_R$, i.e. it takes each value $c\in{\mathbb C}$ at most $p$ times in $D_R$. We consider its Borel transform $$ B(f)
Externí odkaz:
http://arxiv.org/abs/1909.04918
We study rectangular Vandermonde matrices $\mathbf{V}$ with $N+1$ rows and $s$ irregularly spaced nodes on the unit circle, in cases where some of the nodes are "clustered" together -- the elements inside each cluster being separated by at most $h \l
Externí odkaz:
http://arxiv.org/abs/1909.01927
We consider the problem of stable recovery of sparse signals of the form $$F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, $$ from their spectral measurements, known in a bandwidth $\Omega$ with absolute error not exceed
Externí odkaz:
http://arxiv.org/abs/1904.09186
We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary "off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle), in the case when some of the nodes are sep
Externí odkaz:
http://arxiv.org/abs/1809.00658
We start a systematic study of the topology, geometry and singularities of the Prony varieties $S_q(\mu)$, defined by the first $q+1$ equations of the classical Prony system $$\sum_{j=1}^d a_j x_j^k = \mu_k, \ k= 0,1,\ldots \ .$$ Prony varieties, bei
Externí odkaz:
http://arxiv.org/abs/1806.02204
Autor:
Goldman, Gil, Yomdin, Yosef
We consider the reconstruction of spike train signals of the form $$F(x) = \sum_{i=1}^d a_i \delta(x-x_i),$$ from their moments measurements $m_k(F)=\int x^k F(x) dx = \sum_{i=1}^d a_ix^k$. When some of the nodes $x_i$ near collide the inversion beco
Externí odkaz:
http://arxiv.org/abs/1803.09243