Radiation Conditions and Integral Representations for Clifford Algebra-Valued Null-Solutions of the Helmholtz Operator
- 作者: Marmolejo-Olea E.1, Mitrea I.2, Mitrea D.3, Mitrea M.3
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隶属关系:
- Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México
- Department of Mathematics, Temple University
- Department of Mathematics, University of Missouri
- 期: 卷 231, 编号 3 (2018)
- 页面: 367-472
- 栏目: 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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详细
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.
作者简介
E. Marmolejo-Olea
Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México
Email: imitrea@temple.edu
墨西哥, A.P. 273-3 Admon. 3, Cuernavaca, Morelos, 62251
I. Mitrea
Department of Mathematics, Temple University
编辑信件的主要联系方式.
Email: imitrea@temple.edu
美国, 1805 N. Broad Street, Philadelphia, PA, 19122
D. Mitrea
Department of Mathematics, University of Missouri
Email: imitrea@temple.edu
美国, Columbia, MO, 65211
M. Mitrea
Department of Mathematics, University of Missouri
Email: imitrea@temple.edu
美国, Columbia, MO, 65211