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Characterization of colombeau generalized functions by their pointvalues
Author(s) -
Oberguggenberger M.,
Kunzinger M.
Publication year - 1999
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/mana.1999.3212030110
Subject(s) - mathematics , characterization (materials science) , generalized function , pure mathematics , materials science , nanotechnology
A new characterization of elements of Colombeau — type algebras of generalized functions is presented. Since Colombeau functions are not uniquely determined by their pointvalues as defined in [1], [2], a concept of generalized points suitable for securing such a pointvalue description is introduced. This characterization provides an affirmative answer to an open question in the theory of algebras of generalized functions and enables a direct transfer of methods from classical analysis to generalized functions.