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5 papers · 1 filter
Harmonic and monogenic functions on toroidal domains
Z. Ashtab, J. Morais, R. Michael Porter
A standard technique for producing monogenic functions is to apply the adjoint quaternionic Fueter operator to harmonic functions. We will show that this technique does not give a…
Reduced-quaternion inframonogenic functions on the ball
C. Álvarez, J. Morais, R. Michael Porter
A function from a domain in to the quaternions is said to be inframonogenic if , where $\overline{\partial} = \par…
Quaternionic metamonogenic functions in the unit disk
J. Morais, R. Michael Porter
We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+λ)$ for diverse ) in the unit disk, such that every metamonogenic function is approximable…
Reduced-quaternionic Mathieu functions, time-dependent Moisil-Teodorescu operators, and the imaginary-time wave equation
João Morais, R. Michael Porter
We construct a one-parameter family of generalized Mathieu functions, which are reduced quaternion-valued functions of a pair of real variables lying in an ellipse, and which we ca…
Relations among spheroidal and spherical harmonics
Raybel García-Ancona, João Morais, R. Michael Porter
A contragenic function in a domain is a reduced-quaternion-valued (i.e. the last coordinate function is zero) harmonic function, which is orthogonal in $L^…