Hi! I wish to find Fourier coefficients satisfying

(1)

(2)

(3)

(4)

(5)

Here, and are unknown coefficients, and are known coefficients, and is a periodic set in with periodicity , and is defined by eq. (5). The sum in eq. (1) and (4) runs over integers according to eq. (2). My actual problem is two dimensional. Hence, the sums are over and , and the set is defined in two dimensions. I don't know if this changes the problem very much. I'm thankful for any help at all.