8 citations · 18 across the 4 of their papers we have counts for
7 papers
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…
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^…
Hilbert transform for the three-dimensional Vekua equation
Briceyda B. Delgado, R. Michael Porter
The three-dimensional Hilbert transform takes scalar data on the boundary of a domain in R3 and produces the boundary value of the vector part of a quaternionic monogenic (hyperhol…
Spectral parameter power series for arbitrary order linear differential equations
Vladislav V. Kravchenko, R. Michael Porter, Sergii M. Torba
Let be the -th order linear differential operator with variable coefficients. A representation is given for linearly ind…
General solution of the inhomogenous div-curl system and consequences
Briceyda B. Delgado, R. Michael Porter
We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in . An explicit general sol…