Related papers: Simultaneous approximation of translation operator…
We take advantage of the combinatorial interpretations of many sequences of polynomials of binomial type to define a sequence of symmetric functions corresponding to each sequence of polynomials of binomial type. We derive many of the…
We establish $L^p$-type universal approximation theorems for general and non-anticipative functionals on suitable rough path spaces, showing that linear functionals acting on signatures of time-extended rough paths are dense with respect to…
There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to…
We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that…
We develop an approximation theory in Hilbert spaces that generalizes the classical theory of approximation by entire functions of exponential type. The results advance harmonic analysis on manifolds and graphs, thus facilitating data…
In this short note we present some new results concerning cotype and absolutely summing multilinear operators.
We study the action of translation operators on wavelet subspaces. This action gives rise to an equivalence relation on the set of all wavelets. We show by explicit construction that each of the associated equivalence classes is non-empty.
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerged in this context are…
In this paper we study extensions of commuting tuples of symmetric and isometric operators to commuting tuples of self-adjoint and unitary operators. Some conditions which ensure the existence of such extensions are presented. A…
On a separable C*-algebra A every (completely) bounded map, which preserves closed two sided ideals, can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections…
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…
Generalizing classical results of the theory of absolutely summing operators, in this paper we characterize the duals of a quite large class of Banach operator ideals defined or characterized by the transformation of vector-valued…
Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of…
The paper proposes an artificial neural network (ANN) being a global approximator for a special class of functions, which are known as generalized homogeneous. The homogeneity means a symmetry of a function with respect to a group of…
We prove that if an amenable operator algebra is nearly contained in a complemented dual operator algebra, then it can be embedded inside this dual operator algebra via a similarity. The proof relies on a B.E. Johnson Theorem on…