Commuting differential operators with symbols ∂21 + ∂22, ∂21∂22 are related to the functional equation V1(x1)U+(x1 + x2) + V1(x1)U-(x1 - x2) + V2(x2)U+(x1 + x2) - V2(x2)U-(x1 - x2) = F-(x1 + x2) + F-(x1 - x2) + G1(x1) + G2(x2). We discuss several properties, such as a meromorphic extension of solutions and periodicity, of this functional equation and commuting differential operators.
!!!All Science Journal Classification (ASJC) codes
- 数学 (全般)