TY - JOUR
T1 - On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation
AU - Bory Reyes, Juan
AU - Abreu Blaya, Ricardo
AU - Rodríguez Dagnino, Ramón Martin
AU - Kats, Boris Aleksandrovich
N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2019/3/4
Y1 - 2019/3/4
N2 - The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R 2 . Our analysis is based on a suitable operator calculus.
AB - The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R 2 . Our analysis is based on a suitable operator calculus.
KW - Boundary value problems
KW - Helmholtz equations
KW - Quaternionic analysis
UR - http://www.scopus.com/inward/record.url?scp=85063620476&partnerID=8YFLogxK
U2 - 10.1007/s13324-018-0210-3
DO - 10.1007/s13324-018-0210-3
M3 - Artículo
SN - 1664-2368
VL - 9
SP - 483
EP - 496
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 1
ER -