D-holomorphic Functions
The function f is called D-holomorphic when
- 0 = (∂/∂x − j ∂/∂y) ( u + j v)
- = ux − j2 vy + j (vx − uy ).
The consequent partial differential equations are called "Scheffers' conditions" by Isaak Yaglom who credits Georg Scheffers' work of 1893. See Duren's text for the use of similar differential operators to establish the relation of harmonic function theory to analytic functions on the ordinary complex plane C .It is apparent that the components u and v of a D-holomorphic function f satisfy the wave equation, associated with D'Alembert, whereas components of C-holomorphic functions satisfy Laplace's equation.
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