The Dirac Complex on Abstract Vector Variables: Megaforms

REFERENCES

• Adams , W. W. , Berenstein , C. A. , Loustaunau , P. , Sabadini , I. and Struppa , D. C. 1999 . “Regular Functions of Several Quaternionic Variables and the Cauchy-Fueter Complex.” . J. Geom. Anal. , 9 : 1 – 16 . [Adams et al. 99]
   Web of Science ®Google Scholar
• Adams , W. W. and Loustaunau , P. 1994 . An Introduction to Grobner Basis, Graduate Studies in Mathematics Volume 3 , Providence , RI : Amer. Math. Soc. . [Adams and Loustaunau 94]
   Google Scholar
• Adams , W. W. and Loustaunau , P. 2001 . “Analysis of the Module Determining the Properties of Regular Functions of Several Quaternionic Variables.” . Pacific J. , 196 : 1 – 15 . [Adams and Loustaunau 01]
   Web of Science ®Google Scholar
• Adams , W. W. , Loustaunau , P. , Palamodov , V. and Struppa , D. C. 1997 . “Hartog's Phenomenon for Polyregular Functions and Projective Dimension of Related Modules.” . Ann. Inst Fourier , 47 : 623 – 640 . [Adams et al. 97]
   Web of Science ®Google Scholar
• Baston , R. J. 1992 . “Quaternionic Complexes.” . J. Geom. Phys. , 8 ( 1–4 ) : 29 – 52 . [Baston 92]
   Google Scholar
• Berenstein , C. A. , Sabadini , I. and Struppa , D. C. 1996 . Boundary Values of Regular Functions of Quaternionic Variables Volume 347 , Harlow : Longman Scientific and Technical. . [Berenstein et al. 96], Pitman Res. Notes in Math. Ser.
   Google Scholar
• Brackx , F. , Delanghe , R. and Sommen , F. 1982 . Clifford Analysis Volume 76 , Harlow : Longman Scientific and Technical. . [Brackx et al. 82], Pitman Res. Notes in Math.
   Google Scholar
• Colombo , F. , Sabadini , I. , Sommen , F. and Struppa , D. C. 2003 . Analysis of Dirac Systems and Computational Algebra Cambridge , MA : Birkhäuser Verlag. . [Colombo et al. 03], Progress in Mathematical Physics, (in preparation)
   Google Scholar
• Constales , D. 1989 . “The Relative Position of L ²-Domains in Complex and Clifford Analysis.” , PhD thesis State Univ. Ghent. . [Constales 89]
   Google Scholar
• Delanghe , R. , Sommen , F. and Součnek , V. 1992 . Clifford Algebra and Spinor Valued Functions: A Function Theory for the Dirac Operator Volume 53 , Dordrecht : Kluwer Acad. Publ. . [Delanghe et al. 92], Math, and its Appl.
   Google Scholar
• Ehrenpreis , L. 1970 . Fourier Analysis in Several Complex Variables. New York : Wiley-Interscience Publ. . [Ehrenpreis 70]
   Google Scholar
• Gilbert , J. and Murray , M. 1990 . Clifford Algebras and Dirac Operators in Harmonic Analysis. Cambridge , , UK : Cambridge Univ. Press. . [Gilbert and Murray 90]
   Google Scholar
• Hestenes , D. and Sobczyk , G. 1985 . Clifford Algebra to Geometric Calculus. Dordrecht : D. Reidel. . [Hestenes and Sobczyk 85]
   Google Scholar
• Komatsu , H. 1973 . “Relative Cohomology of Sheaves of Solutions of Differential Equations.” . In Hyperfunctions and Pseudo-Differential Equations Edited by: Komatsu , H. Volume 287 , 196 – 261 . Berlin-Heidelberg : Springer-Verlag. . [Komatsu 73], Lecture Notes in Mathematics
   Google Scholar
• Krantz , S. 1992 . Function Theory of Several Complex Variables. Belmont , CA : Wadsworth and Brooks/Cole. . [Krantz 83]
   Google Scholar
• Laville , G. 1983 . “Une famille de solutions de l'equation de Dirac avec champ electromagnetique quelconque.” . C.R. Acad. Sci. Paris , 296 : 1029 – 1032 . [Laville 83]
   Google Scholar
• Palamodov , V. P. 1970 . Linear Differential Operators with Constant Coefficients. New York : Springer Verlag. . [Palamodov 70]
   Google Scholar
• Palamodov , V. V. 1999 . “Holomorphic Synthesis of Monogenic Functions of Several Quaternionic Variables.” . J. Anal. Math. , 78 : 177 – 204 . [Palamodov 99]
   Web of Science ®Google Scholar
• Pertici , D. 1988 . “Funzioni regolari di phú variabili quaternioniche.” . Ann. Mat. Pura Appl., Serie IV , CLI : 39 – 65 . [Pertici 88]
   Web of Science ®Google Scholar
• Sabadini , I. and Struppa , D. C. 1997 . “Some Open Problems on the Analysis of the Cauchy-Fueter System in Several Variables.” . Suk. RIMS Kyoto Univ. , 1001 : 1 – 21 . [Sabadini and Struppa 97]
   Google Scholar
• Sabadini , I. and Struppa , D. C. 2002 . “Computational Algebraic Analysis Methods in Clifford Analysis.” . Math. Methods Appl. Sci. , 25 : 1415 – 1427 . [Sabadini and Struppa 02]
   Web of Science ®Google Scholar
• Sabadini , I. , Sommen , F. , Struppa , D. C. and Van Lancker , P. 2002 . “Complexes of Dirac Operators in Clifford Algebras.” . Math. Z. , 239 ( 2 ) : 293 – 320 . [Sabadini et al. 02]
   Web of Science ®Google Scholar
• Somberg , P. 2001 . “Quaternionic Complexes in Clifford Analysis.” . In Clifford Analysis and its Applications Edited by: Brackx , F. , Chisholm , J. S. R. and Souček , V. 293 – 301 . Dordrecht : Kluwer Acad. Publ. . [Somberg 01], NATO ARW Series
   Google Scholar
• Sommen , F. 1987 . “Martinelli-Bochner Type Formulae in Complex Clifford Analysis.” . Z.A.A. , 6 ( 1 ) : 75 – 82 . [Sommen 87]
   Google Scholar
• Sommen , F. 1997 . “An Algebra of Abstract Vector Variables.” . Portugaliae Mathematica , 54 ( 3 ) : 287 – 310 . [Sommen 97]
   Google Scholar
• Sommen , F. 1999 . “Clifford Analysis in Two and Several Vector Variables.” . Applicable Analysis , 73 : 225 – 253 . [Sommen 99]
   Google Scholar
• Sommen , F. 2001 . “Clifford Analysis on the Level of Abstract Vector Variables.” . In Clifford Analysis and its Applications Edited by: Brackx , F. , Chisholm , J. S. R. and Souček , V. 303 – 322 . Dordrecht : Kluwer Acad. Publ. . [Sommen 01], NATO ARW Series
   Google Scholar
• Struppa , D. C. 1998 . “Grobner Bases in Partial Differential Equations.” . In Gröbner Bases and Applications (Linz, 1998) Volume 251 , 235 – 245 . Cambridge , , UK : Cambridge Univ. Press. . [Struppa 98], London Math. Soc. Lecture Note Ser.
   Google Scholar