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1996 | 37 | 1 | 159-172
Tytuł artykułu

Fundamental solutions for Dirac-type operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
37
Numer
1
Strony
159-172
Opis fizyczny
Daty
wydano
1996
Twórcy
  • Freiberg University of Mining and Technology, Faculty of Mathematics and Computer Science, Institute of Applied Mathematics I, D-09596 Freiberg, Germany
Bibliografia
  • [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.
  • [Be2] S. Bernstein, Cauchy-Green formulas in Clifford Analysis, to appear.
  • [BDS] F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Pitman, Boston- London-Melbourne, 1982.
  • [DL] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 1 and 5, Springer-Verlag, 1992.
  • [GS] K. Gürlebeck and W. Sprößig, Quaternionic Analysis and Elliptic Boundary Value Problems, Akademie-Verlag, Berlin, 1989.
  • [Jan] B. Jancewicz, Multivectors and Clifford Algebra in Electrodynamics, World Scientific Publ. Co. Pt;. Ltd., 1989.
  • [Kr1] V. V. Kravchenko, Integral representation of biquaternionic hyperholomorphic functions and it's application PhD Thesis, Rostov State University, 1993 (Russian).
  • [Kr2] V. V. Kravchenko, On the generalized holomorphic vectors, Abstracts of Republican Research Conference devoted to 200 birth of N.I. Lobachevskij, Odessa, Ukraine, 1992, Part 1, p. 35.
  • [KS1] V. V. Kravchenko and M. V. Shapiro, Hypercomplex factorization of the multidimensional Helmholtz operator and some of its applications, Dokl. Sem. Inst. I.N. Vekua, Tbilisi 5 (1) (1990), 106-109 (Russian).
  • [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.
  • [MP] S. G. Michlin and S. Prößdorf, Singuläre Integraloperatoren, Akademie-Verlag, Berlin, 1980.
  • [Ob1] E. I. Obolashvili, Space analogous of generalized analytic functions, Soobch. Akad. Nauk Gruzin. SSR, 73, 1 (1974), 21-24 (Russian).
  • [Ob2] E. I. Obolashvili, Spatial generalized holomorphic vectors, Different. Uravneniya 11 (1) (1975), 108-115 (Russian).
  • [Ort] N. Ortner, Regularisierte Faltung von Distributionen. Teil 2: Eine Tabelle von Fundamentallösungen, Journal of Applied Mathematics and Physics (ZAMP), 31 (1980), 133-155.
  • [Xu1] Z. Xu, Boundary value problems and function-theory for Spin-invariant differential operators, PhD Thesis, State University of Gent, 1989.
  • [Xu2] Z. Xu, A function theory for the operator D → -λ, Complex Variables Theory Appl., 16 (1) (1991), 27-42.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv37i1p159bwm
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