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Special power series expansions of monogenic functions around surfaces of codimension two
Author(s) -
Peña Peña Dixan,
Sommen Frank
Publication year - 2009
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.1056
Subject(s) - codimension , mathematics , power series , series (stratigraphy) , cauchy distribution , extension (predicate logic) , pure mathematics , spheres , mathematical analysis , paleontology , physics , astronomy , computer science , biology , programming language
Abstract In this paper we will focus on power series expansions around special surfaces of codimension two, in particular around spheres and products of spheres. This will include a version of the Cauchy–Kowalewski extension theorem around these surfaces. This higher codimension result was only obtained so far in the flat case (see Partial Differential Equations with Complex Analysis . Pitman Research Notes Mathematical Series, vol. 262. Longman Science and Technology: Harlow, 1992; 61–92; Mathematics and its Applications , vol. 53. Kluwer Academic Publishers Group: Dordrecht, 1992). Copyright © 2008 John Wiley & Sons, Ltd.