Uniqueness of Multiple Trigonometric Series

Abstract

be a trigonometric series of two variables, where Amn(X, y) = amn cos mx cos ny + bm,n cos mX sin ny + dm,n sin mx cos fy + fm,n sin mx sin ny (m, n = 1, 2, *. . ), Ao ,(x, y) = 1j(aon cos ny + bon sin my) (n = 1, 2, ... ), AmO(x, y) = A(am,o COS mx + dmo sin mx) (m = 1, 2', .), and Ao,o(x, y) Ao0,o/4, amn , brn,n , dm,n , fm,n being real constants. The series (1.1) is said to be convergent (or summable) by spherical means, if the spherical partial sum