Fundamental solutions for Dirac-type operators

Swanhild Bernstein

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 159-172
  • ISSN: 0137-6934

Abstract

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We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces C 1 ( G ) and W p 1 ( G ) . Further, we consider the Cauchy problem for this operator.

How to cite

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Bernstein, Swanhild. "Fundamental solutions for Dirac-type operators." Banach Center Publications 37.1 (1996): 159-172. <http://eudml.org/doc/208593>.

@article{Bernstein1996,
abstract = {We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces $C^1(G)$ and $W_\{p\}^\{1\}(G)$. Further, we consider the Cauchy problem for this operator.},
author = {Bernstein, Swanhild},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {159-172},
title = {Fundamental solutions for Dirac-type operators},
url = {http://eudml.org/doc/208593},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Bernstein, Swanhild
TI - Fundamental solutions for Dirac-type operators
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 159
EP - 172
AB - We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces $C^1(G)$ and $W_{p}^{1}(G)$. Further, we consider the Cauchy problem for this operator.
LA - eng
UR - http://eudml.org/doc/208593
ER -

References

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  1. [Be1] S. Bernstein, Analytische Untersuchungen in unbeschränkten Gebieten mit Anwendungen auf quaternionische Operatortheorie und elliptische Randwertprobleme, PhD Thesis, Freiberg University of Mining and Technology, 1993. 
  2. [Be2] S. Bernstein, Cauchy-Green formulas in Clifford Analysis, to appear. 
  3. [BDS] F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman, Boston- London-Melbourne, 1982. 
  4. [DL] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 1 and 5, Springer-Verlag, 1992. 
  5. [GS] K. Gürlebeck and W. Sprößig, Quaternionic Analysis and Elliptic Boundary Value Problems, Akademie-Verlag, Berlin, 1989. Zbl0699.35007
  6. [Jan] B. Jancewicz, Multivectors and Clifford Algebra in Electrodynamics, World Scientific Publ. Co. Pt;. Ltd., 1989. Zbl0727.15015
  7. [Kr1] V. V. Kravchenko, Integral representation of biquaternionic hyperholomorphic functions and it's application PhD Thesis, Rostov State University, 1993 (Russian). 
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  10. [KS2] V. V. Kravchenko and M. V. Shapiro, Helmholtz operator with a quaternionic wave number and associated function theory, Deformations of Mathematical Structures. Ed. by J. Ławrynowicz, Kluwer Academic Publishers, Dordrecht 1993, 101-128. 
  11. [MP] S. G. Michlin and S. Prößdorf, Singuläre Integraloperatoren, Akademie-Verlag, Berlin, 1980. 
  12. [Ob1] E. I. Obolashvili, Space analogous of generalized analytic functions, Soobch. Akad. Nauk Gruzin. SSR, 73, 1 (1974), 21-24 (Russian). 
  13. [Ob2] E. I. Obolashvili, Spatial generalized holomorphic vectors, Different. Uravneniya 11 (1) (1975), 108-115 (Russian). 
  14. [Ort] N. Ortner, Regularisierte Faltung von Distributionen. Teil 2: Eine Tabelle von Fundamentallösungen, Journal of Applied Mathematics and Physics (ZAMP), 31 (1980), 133-155. 
  15. [Xu1] Z. Xu, Boundary value problems and function-theory for Spin-invariant differential operators, PhD Thesis, State University of Gent, 1989. 
  16. [Xu2] Z. Xu, A function theory for the operator D → -λ, Complex Variables Theory Appl., 16 (1) (1991), 27-42. 

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