Complete systems of Beltrami fields using complex quaternions and transmutation theory

DOI10.1007/s00006-021-01131-wzbMath1464.35004OpenAlexW3156078727MaRDI QIDQ2025769

Pablo E. Moreira, Vladislav V. Kravchenko, R. Michael Porter

Publication date: 17 May 2021

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-021-01131-w

zbMATH Keywords

monogenic functionBeltrami fieldforce-free fieldtransmutation operatorcomplex quaternioncomplete system of solutionsRunge type theorem

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Functions of hypercomplex variables and generalized variables (30G35) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Series solutions to PDEs (35C10)

Related Items (3)

Biquaternionic treatment of inhomogeneous time-harmonic Maxwell's equations over unbounded domains ⋮ Transmutation operators and complete systems of solutions for the radial bicomplex Vekua equation ⋮ A right inverse of curl which is divergence‐free invariant and some applications to generalized Vekua‐type problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving exterior Neumann boundary value problems for Beltrami fields through the Beltrami system
• Quaternionic functions and their applications in a viscous fluid flow
• Transmutations, \(L\)-bases and complete families of solutions of the stationary Schrödinger equation in the plane
• Transmutations d'opérateurs différentiels dans le domaine complexe
• Representations of the Beltrami fields in an isotropic chiral medium with the Drude-Born-Fedorov constitutive relations
• Approximation theorems for the Moisil-Theodorescu system
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• A boundary integral equation method for a Neumann boundary problem for force-free fields
• A remark on a boundary value problem for force-free fields
• The method of fundamental solutions for elliptic boundary value problems
• Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions
• Analytic approximation of solutions of parabolic partial differential equations with variable coefficients
• Quaternionic fundamental solutions for electromagnetic scattering problems and application
• Complete families of solutions for the Dirac equation using bicomplex function theory and transmutations
• \(T\)- and \(D\)-matrix methods for electromagnetic scattering by impedance obstacles
• Beltrami vector fields with an icosahedral symmetry
• A right inverse operator for \(\operatorname{curl}+\lambda \) and applications
• Force-free magnetic fields in resistive magnetohydrostatics
• Complete systems of recursive integrals and Taylor series for solutions of Sturm-Liouville equations
• Transmutations for Darboux transformed operators with applications
• Applied Pseudoanalytic Function Theory
• The treatment of a Neumann boundary value problem for force-free fields by an integral equation method
• On Beltrami fields with nonconstant proportionality factor
• Quaternionic factorization of the Schrödinger operator and its applications to some first-order systems of mathematical physics
• Quaternionic Approximation
• Transmutations and Spectral Parameter Power Series in Eigenvalue Problems
• Direct and Inverse Sturm-Liouville Problems
• Transmutation operators and complete systems of solutions for the radial Schrödinger equation
• Solution of parabolic free boundary problems using transmuted heat polynomials
• Regular quaternionic polynomials and their properties
• On some properties of Beltrami fields in chiral media.

This page was built for publication: Complete systems of Beltrami fields using complex quaternions and transmutation theory