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Fischer decomposition and special solutions for the parabolic Dirac operator
Author(s) -
Cerejeiras P.,
Sommen F.,
Vieira N.
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.825
Subject(s) - dirac operator , mathematics , homogeneity (statistics) , dirac algebra , clifford analysis , operator (biology) , homogeneous , parabolic partial differential equation , dirac (video compression format) , mathematical analysis , dirac equation , mathematical physics , pure mathematics , partial differential equation , quantum mechanics , combinatorics , physics , chemistry , biochemistry , statistics , repressor , transcription factor , neutrino , gene
In this paper we study a Fischer decomposition for the parabolic Dirac operator which factorizes the heat equation. Since the standard construction techniques are not valid in our case, due to the non‐homogeneity of the positive parabolic Dirac operator, we first establish and study the Fischer decomposition for the homogeneous part of the parabolic Dirac operator. Finally, we construct null‐solutions of the parabolic Dirac operator by means of series expansions in terms of cylindrical co‐ordinates. Copyright © 2006 John Wiley & Sons, Ltd.