Conjugate complex harmonic functions

Conjugate Harmonic Functions and Clifford Algebras

We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions.

Classical Expansions and Their Relation to Conjugate Harmonic Functions

On the conjugate of periodic piecewise harmonic functions

The paper considers the conjugate of periodic functions which are piecewise harmonic. In particular, we consider the harmonic conjugate of the solution of the problem of stationary heat conduction through a periodic network of fibres and matrix of arbitrary shape. A numerical example is also presented.

Complex-conjugate-resolved imaging using two-harmonic FD-OCT

The two-harmonic FD-OCT method, where the quadrature components of the spectral interferogram are obtained by simultaneous acquisition of the first and second harmonics of the phase-modulated interferogram, is used for complexconjugate-resolved imaging of biological samples. The method is implemented using sampling of the phase modulated interferogram with an integrating detector array followed...

Valence of Complex-valued Planar Harmonic Functions

The valence of a function f at a point w is the number of distinct, finite solutions to f(z) = w. Let f be a complex-valued harmonic function in an open set R ⊆ C. Let S denote the critical set of f and C(f) the global cluster set of f . We show that f(S)∪C(f) partitions the complex plane into regions of constant valence. We give some conditions such that f(S) ∪ C(f) has empty interior. We also...