On functional equations of the multiplicative type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Chavez, Esteban A.²  Sahoo, Prasanna K.¹ 

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Univ Calif Santa Barbara, Dept Appl Probabil & Stat, Santa Barbara, CA 93106 USA

关键词: Determinant;    Functional equation;    Linear transformation;    Matrix diagonalization;    Multiplicative function;    Permanent;   

DOI  :  10.1016/j.jmaa.2015.05.060

来源: Elsevier

【 摘 要 】

This paper aims to determine the general solution f : F-2 -> S of the equation f(phi (x, y, u, v) = f (x, y) f (u, v) for suitable conditions on the function phi: F-4 -> F-2, where F will denote either R or C, and S is a multiplicative semigroup. Using this result, we determine the general solution of several functional equations studied earlier, namely f (ux + vy, uy + vx) = f (x, y) f (u, v); f (ux + (lambda - 1)vy, vx + uy + (lambda - 2)vy) = f (x, y) f (u, v); f (ux - vy, uy - vx) = f (x, y) f (u, v); f (ux + vy, uy vx) = f (x, y) f (u, v); f (up; + vy, uy - vx) = f (x, y) f (v, u); and f (ux - vy,, uy+v(x+y)) = f (x, y) f(u, v). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free