摘要：In this paper, we consider the following generalized quadratic functional equation with n-independent variables in the spaces of generalized functions: ∑ 1 ≤ i < j ≤ n ( f ( x i + x j ) + f ( x i − x j ) ) = 2 ( n − 1 ) ∑ i = 1 n f ( x i ) . Making use of the fundamental solution of the heat equation, we solve the general solutions and the stability problems of the above equation in the spaces of tempered distributions and Fourier hyperfunctions. Moreover, using the Dirac sequence of regularizing functions, we extend these results to the space of distributions. MSC:39B82, 46F05.
关键词：quadratic functional equation ; stability ; generalized function ; heat kernel ; Gauss transform ; distribution
