Wilson's functional equations on groups

We study properties of solutionsf, g, h C(G) of the functional equation

Generalized sine equations,II

In this paper we solve the equations

On functional equations associated with characters of unitary representations of groups

This is mainly concerned with the following functional equation:

On a joint generalization of Cauchy's and d'Alembert's functional equations

LetX be a locally compact abelian group and let a compact groupG act onX. We find solutionsf: X inL(X) of the following functional equation:

On the general solution of a nonsymmetric partial difference functional equation analogous to the wave equation

We give the general solution of the nonsymmetric partial difference functional equationf(x + t,y) + f(x – t,y) – 2f(x,y)/t ² =f(x,y + s) + f(x,y – s) – 2f(x,y)/s ² (N) analogous to the well-known wave equation ( ²/x ² – ²/y ²)f(x,y) = 0 with the aid of generalized polynomials when no regularity assumptions are imposed onf. The result is as follows. Theorem.Let R be the set of all real numbers. A function f: R × R R satisfies the functional equation (N)for all x, y R, s, t R\{0}, and s t if and only if there exist

On the quasiarithmetic mean in a mean value property and the associated functional equation

The functional equation

Oscillating solutions of integral equations and linear recursions

Answering a question of Z. Daróczy we show that there are positive sequences _n satisfying the recursion

The Binet-Pexider functional equation for rectangular matrices

IfK is a field of characteristic 0 then the following is shown. Iff, g, h: M _n (K) K are non-constant solutions of the Binet—Pexider functional equation

An oscillation criterion for functional differential equations with deviating arguments

An oscillation criterion is given for the differential equation

Rational approximation to Lipschitz and Zygmund classes

In this paper, characterizations for lim _n(R _n (f)/(n ^–1)=0 inH and for lim _n(n ^r+ R _n (f)=0 inW ^r Lip ,r1, are given, while, forZ, a generalization to a related result of Newman is established.Communicated by Ronald A. DeVore.     

An extension of the Erdős-Stone theorem

LetK _p(u₁, ..., u_p) be the completep-partite graph whoseith vertex class hasu _i vertices (lip). We show that the theorem of Erds and Stone can be extended as follows. There is an absolute constant >0 such that, for allr1, 0<1 and=">1/r, every graphG=G ⁿ of sufficiently large order |G|=n with at least

On the derivability of Lipschitz functions

We show that given any Borel measure onR, every Lipschitz function is μ-a.e. differentiable with respect to μ.     

Periodic boundary value problem of functional differential equations with perturbation

By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation     

On the rapidly decreasing solutions for some systems of differential equations with unbounded coefficients

In this paper we continue the study of solvability of the non-homogeneous system of linear differential equations

Power series and zeroes of trinomial equations

In this paper we show how power series can be used to obtain solutions of trinomial equations

A new Pythagorean functional equation

The purpose of this paper is to solve the following Pythagorean functional equation:(e ^p(x,y) ) ² ) = q(x,y) ² + r(x, y) ², where each ofp(x,y), q(x, y) andr(x, y) is a real-valued unknown harmonic function of the real variablesx, y on the wholexy-planeR ².The result is as follows.     

On solving implicit differential equations on parallel computers

We construct and analyse integration methods for solving initial value problems for implicit differential equations (IDEs) that can be efficiently used on parallel computer systems. We construct an IDE method for general IDEs of arbitrarily high index, and two methods that can be applied to partitioned IDEs. The partitioned IDE methods both exploit the special form of the problem and converge faster than the general IDE method. The first partitioned IDE method is suitable for higher-index problems, the second partitioned IDE method only applies to index 1 problems, but is considerably less expensive on parallel computers. This paper presents the results presented in June 1995 at the Seminario Matematico e Fisico organized by the Mathematics Department of the Polytechnics University of Milano. Conferenza tenuta da P.J. van der Houwen il 5 giugno 1995     

On very weak entire solutions of nonlinear partial differential equations

Let us consider the variational equation in R ⁿ

On a generalized asymptotic mean value property

In this paper we study the spaces of continuous functionsf on ² satisfying