Wilson’s functional equation for vector and matrix functions

Vector functional-difference equation in electromagnetic scattering

A vector functional-difference equation of the first order with a special matrix coefficient is analysed. It is shown how it can be converted into a Riemann-Hilbert boundary-value problem on a union of two segments on a hyperelliptic surface. The genus of the surface is defined by the number of zeros and poles of odd order of a characteristic function in a strip. An even solution of a symmetric...

Stability of a 2-Dimensional Functional Equation in a Class of Vector Variable Functions

In 1940, Ulam proposed the stability problem see 1 : Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1 then there is a homomorphism H : G1 → G2 with d h x ,H x < ε for all x ∈ G1? In 1941, this problem was solved by Hyers 2 in the case of...

Generalized matrix functions, determinant and permanent

In this paper, using permutation matrices or symmetric matrices, necessary and sufficient conditions are given for a generalized matrix function to be the determinant or the permanent. We prove that a generalized matrix function is the determinant or the permanent if and only if it preserves the product of symmetric permutation matrices. Also we show that a generalized matrix function is the de...

A functional equation with two unknown functions

Differential Equation of Sensitivity Matrix for Final Velocity Constraint