Аннотация:From the point of view of analytic complexity theory, all harmonic functions of two
variables split into three classes: functions of complexity zero, one, and two. Only linear functions
of one variable have complexity zero. This paper contains a complete description of simple
harmonic functions, i.e., of functions of analytic complexity one. These functions constitute a
seven-dimensional family expressible as integrals of elliptic functions. All other harmonic functions
have complexity two and are, in this sense, of higher complexity. Solutions of the wave equation, the
heat equation, and the Hopf equation are also studied.
Keywords: analytical complexity, harmonic function, elliptic function.