11 citations · 11 across the 3 of their papers we have counts for
6 papers
The Bergman kernel for the Vekua equation
Hugo M. Campos, Vladislav V. Kravchenko
The paper extends some well-known results for analytic functions onto solutions of the Vekua equation regarding the existence and const…
Standard transmutation operators for the one dimensional Schrödinger operator with a locally integrable potential
Hugo M Campos
We study a special class of operators T satisfying the transmutation relation (Tu)"-qTu=Tu" in the sense of distributions, where q is a locally integrable function, and u belongs t…
Spectral parameter power series method for discontinuous coefficients
Herminio Blancarte, Hugo M. Campos, Kira V. Khmelnytskaya
Let (a,b) be a finite interval and 1/p, q, r be functions from L1(a,b). We show that a general solution (in the weak sense) of the equation (pu')'+qu = zru on (a,b) can be construc…
Fundamentals of bicomplex pseudoanalytic function theory: Cauchy integral formulas, negative formal powers and Schrödinger equations with complex coefficients
Hugo M. Campos, Vladislav V. Kravchenko
The study of the Dirac system and second-order elliptic equations with complex-valued coefficients on the plane leads to bicomplex Vekua equations. To the difference of complex pse…
Complete families of solutions for the Dirac equation: an application of bicomplex pseudoanalytic function theory and transmutation operators
Hugo M. Campos, Vladislav V. Kravchenko, Luis M. Mendez
The Dirac equation with a scalar and an electromagnetic potentials is considered. In the time-harmonic case and when all the involved functions depend only on two spatial variables…
Transmutations, L-bases and complete families of solutions of the stationary Schrödinger equation in the plane
Hugo M. Campos, Vladislav V. Kravchenko, Sergii M. Torba
An L-basis associated to a linear second-order ordinary differential operator L is an infinite sequence of functions {ϕ_k}_{k=0}^{\infty} such that Lϕ_k=0 for k=0,1, Lϕ_k=k(k-1)ϕ_{…