Related papers: Rational approximation of holomorphic semigroups r…

We show that a bounded analytic semigroup on an $L_p$-space has a bounded $H^{\infty}(\Sigma_{\varphi})$-calculus for some $\varphi < \frac{\pi}{2}$ if and only if the semigroup can be obtained, after restricting to invariant subspaces,…

Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups:…

We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.

We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by…

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a…

We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banach spaces.

Stochastic Approximation (SA) was introduced in the early 1950's and has been an active area of research for several decades. While the initial focus was on statistical questions, it was seen to have applications to signal processing,…

We study the functional calculus properties of generators of $C_{0}$-groups under type and cotype assumptions on the underlying Banach space. In particular, we show the following. Let $-iA$ generate a $C_{0}$-group on a Banach space $X$…

We obtain the result of approximating \( f \) in the \( H^1(\mathbb{R}) \) norm using partial Hausdorff integrals. Specifically, by leveraging the homogeneous multiplier theory of \( H^1(\mathbb{R}) \) and the \( K \) functional theory, one…

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the…

In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…

The paper describes homomorphisms between Douglas algebras and some semisimple Banach algebras. The main tool is a result on the structure of the space $C(Z,\mathfrak M)$ of continuous mappings from a connected first-countable $T_1$ space…

We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.

Let $H^\infty(\mathbb D\times\N)$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk $\mathbb D\subset\mathbb C$. We show that the dense stable rank of…

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The…

Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…

Let f be holomorphically continuable over the complex plane except for finitely many branch points contained in the unit disk. We prove that best rational approximants to f of degree n, in the L^2-sense on the unit circle, have poles that…