Radiation Conditions and Integral Representations for Clifford Algebra-Valued Null-Solutions of the Helmholtz Operator
- Autores: Marmolejo-Olea E.1, Mitrea I.2, Mitrea D.3, Mitrea M.3
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Afiliações:
- Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México
- Department of Mathematics, Temple University
- Department of Mathematics, University of Missouri
- Edição: Volume 231, Nº 3 (2018)
- Páginas: 367-472
- Seção: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241154
- DOI: https://doi.org/10.1007/s10958-018-3826-9
- ID: 241154
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Resumo
The goal of this paper is to develop a unified approach to radiation conditions for the entire class of null-solutions of the Helmholtz operator which are Clifford algebra-valued. The latter is an algebraic context which permits the simultaneous consideration of scalarvalued and vector-valued functions, as well as differential forms of any mixed degree. In such a setting, we provide a multitude of novel radiation conditions which naturally contain the classical Sommerfeld and Silver–Müller radiation conditions in the case of null-solutions for the scalar Helmholtz operator and the Maxwell system respectively, and which also encompass as a particular case the radiation condition introduced by McIntosh and Mitrea for perturbed Dirac operators.
Sobre autores
E. Marmolejo-Olea
Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México
Email: imitrea@temple.edu
México, A.P. 273-3 Admon. 3, Cuernavaca, Morelos, 62251
I. Mitrea
Department of Mathematics, Temple University
Autor responsável pela correspondência
Email: imitrea@temple.edu
Estados Unidos da América, 1805 N. Broad Street, Philadelphia, PA, 19122
D. Mitrea
Department of Mathematics, University of Missouri
Email: imitrea@temple.edu
Estados Unidos da América, Columbia, MO, 65211
M. Mitrea
Department of Mathematics, University of Missouri
Email: imitrea@temple.edu
Estados Unidos da América, Columbia, MO, 65211