Related papers: Integral representation of functions on the circle
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n,s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by the multivariate sigma function. This expression is…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
Multivariable, real-valued functions induce matrix-valued functions defined on the space of d-tuples of n-times-n pairwise-commuting self-adjoint matrices. We examine the geometry of this space of matrices and conclude that the best notion…
A rational homogeneous (of degree one) positive real matrix-valued function is presented as the Schur complement of a block of the linear pencil with positive semidefinite matrix coefficients. The partial derivative numerators of a rational…
This is an elementary introduction to infinite-dimensional probability. In the lectures, we compute the exact mean values of some functionals on C[0,1] and L[0,1] by considering these functionals as infinite-dimensional random variables.…
Positive definite functions on spheres have received an increasing interest in many branches of mathematics and statistics. In particular, the Schoenberg sequences in the spectral representation of positive definite functions have been…
Hybrid systems can express a plethora of physical phenomena and systems as they can combine continuous and discrete dynamics. There exist several tools that enable the reachability analysis of hybrid systems modeled as hybrid automata.…
We prove that the Krull dimension of the ring of holomorphic functions of a connected complex manifold is at least continuum if it is positive.
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asympotic formula for the number of representations of an integer in this form. The result…
The aim of this paper is to give an algebraic characterization of the rings $C(X,\mathbb{Q}_p)$ of all continuous $\mathbb{Q}_p$-valued functions on a compact space $X$. The characterization is similar to that of M. Stone from 1940 for the…
A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.
We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…
We show that a certain integral representation of the one-sided Skorokhod reflection of a continuous bounded variation function characterizes the reflection in that it possesses a unique maximal solution which solves the Skorokhod…
This is a survey on best polynomial approximation on the unit sphere and the unit ball. The central problem is to describe the approximation behavior of a function by polynomials via smoothness of the function. A major effort is to identify…
We show that any decoherence functional $D$ can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural…
In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to ${\bf L}^1$-distance.
For a rational function f we consider the norm of the derivative with respect to the spherical metric and denote by K(f) the supremum of this norm. We give estimates of this quantity K(f) both for an individual function and for sequences of…
We prove that every vertically nearly separately continuous function defined on a product of a strong PP-space and a topological space and with values in a strongly $\sigma$-metrizable space with a special stratification, is a pointwise…