TY - GEN

T1 - MR3377117 Reviewed Giordano, Paolo; Nigsch, Eduard A. Unifying order structures for Colombeau algebras. Math. Nachr. 288 (2015), no. 11-12, 1286–1302. (Reviewer: Francesco Tschinke)

AU - Tschinke, Francesco

PY - 2015

Y1 - 2015

N2 - Colombeau Algebras are differential algebras of generalized functions (that includethe space of distributions) that are defined using a quotient set procedure involvingparticular classes of nets in a basic space E = (C∞(Ω))A, where Ω is an open subset ofRn and A is an index set. The choice of such nets depends mainly on their asymptoticbehavior over a suitable index set A. Many variants of Colombeau Algebras existingin the literature occur mainly due to different choices of the index set (and to thechoice of asymptotic behavior). A purpose of this paper is to formally unify some ofthese algebras, redefining the asymptotic behavior on an abstract (pre-ordered) set ofindices, and generalizing the corresponding “Landau big-O” notion. Such notions arereformulated in order to simplify the definition of diffeomorphism invariant algebra andto generalize some theorems which hold in the case of a special algebra

AB - Colombeau Algebras are differential algebras of generalized functions (that includethe space of distributions) that are defined using a quotient set procedure involvingparticular classes of nets in a basic space E = (C∞(Ω))A, where Ω is an open subset ofRn and A is an index set. The choice of such nets depends mainly on their asymptoticbehavior over a suitable index set A. Many variants of Colombeau Algebras existingin the literature occur mainly due to different choices of the index set (and to thechoice of asymptotic behavior). A purpose of this paper is to formally unify some ofthese algebras, redefining the asymptotic behavior on an abstract (pre-ordered) set ofindices, and generalizing the corresponding “Landau big-O” notion. Such notions arereformulated in order to simplify the definition of diffeomorphism invariant algebra andto generalize some theorems which hold in the case of a special algebra

UR - http://hdl.handle.net/10447/325650

UR - https://mathscinet.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=RVCN&pg5=TI&pg6=RVCN&pg7=ALLF&pg8=ET&review_format=html&s4=tschinke&s5=&s6=&s7=&s8=All&sort=Newest&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=9&mx-pid=3377117

M3 - Other contribution

ER -