Related papers: Representation and Superposition of Discrete Funct…
Every continuous function of two or more real variables can be written as the superposition of continuous functions of one real variable along with addition.
We present a well-structured detailed exposition of a well-known proof of the following celebrated result solving Hilbert's 13th problem on superpositions. For functions of 2 variables the statement is as follows. Kolmogorov Theorem. There…
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
Every one knows that an equation is equivalent to a multivariate function. Generally speaking, there are more than one unknown x in this multivariate function and it is not easy to reduce the number of unknown x to one. In this paper we…
An ordinary differential equation is said to have a superposition formula if its general solution can be expressed as a function of a finite number of particular solution. Nonlinear ODE's with superposition formulas include matrix Riccati…
This preprint is dedicated to a self contained simple proof of the classical criteria for representability of algebraic functions of several complex variables by radicals. It also contains a criteria for representability of algebroidal…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3,2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of…
In a number of papers, Y. Sternfeld investigated the problems of representation of continuous and bounded functions by linear superpositions. In particular, he proved that if such representation holds for continuous functions, then it holds…
In this thesis we study three problems. The first is the superposition of the operators and their proprities, such as boundedness,continuity,regularity and the inequalities of the norms of the composition of functions in some functional…
We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are…
Consider the discrete cubic Hilbert transform defined on finitely supported functions $f$ on $\mathbb{Z}$ by \begin{eqnarray*} H_3f(n) = \sum_{m \not = 0} \frac{f(n- m^3)}{m}. \end{eqnarray*} We prove that there exists $r <2$ and universal…
A unified approach to the representation of solutions of linear PDE's with constant coefficients in high dimensions in terms of solutions of the same PDE's in lower dimensions is presented. It is based on the observation that if a function…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…
An arbitrary linear relation (multivalued operator) acting from one Hilbert space to another Hilbert space is shown to be the sum of a closable operator and a singular relation whose closure is the Cartesian product of closed subspaces.…
We consider the problem of the representation of real continuous functions by linear superpositions $\sum_{i=1}^{k}g_{i}\circ p_{i}$ with continuous $g_{i}$ and $p_{i}$. This problem was considered by many authors. But complete, and at the…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…
We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two…
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special…