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Plemelj Projection Operators over Domain Manifolds
Author(s) -
Ryan John
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200103)223:1<89::aid-mana89>3.0.co;2-#
Subject(s) - mathematics , projection (relational algebra) , domain (mathematical analysis) , pure mathematics , mathematical analysis , algorithm
Plemelj projection operators are introduced for spaces of square integrable functions defined over the boundaries of a class of compact real n – dimensional manifolds lying in ℂ n . These manifolds possess many properties similar to domains in ℝ n , and are consequently called domain manifolds. The key ingredients used here are techniques from both real and complex Clifford analysis. Analogues of the Kerzman – Stein kernel and Szegö projection operators are introduced, and their conformal covariance is described.