TY - CHAP

T1 - A new nonformal noncommutative calculus

T2 - Associativity and finite part regularization

AU - Omori, Hideki

AU - Maeda, Yoshiaki

AU - Miyazaki, Naoya

AU - Yoshioka, Akira

PY - 2008/10/1

Y1 - 2008/10/1

N2 - We interpret the element 1/2ih (u * v + v * u) in the generators u, v of the Wey1 algebra W2 as an indeterminate in N+ 1/2 or -(N+ 1/2), using methods of the transcendental calculus outlined in the announcement [13]. The main purpose of this paper is to give a rigorous proof for the part of [13] which introduces this indeterminate phenomenon. Namely, we discuss how to obtain associativity in the transcendental calculus and show how the Hadamard finite part procedure can be implemented in our context.

AB - We interpret the element 1/2ih (u * v + v * u) in the generators u, v of the Wey1 algebra W2 as an indeterminate in N+ 1/2 or -(N+ 1/2), using methods of the transcendental calculus outlined in the announcement [13]. The main purpose of this paper is to give a rigorous proof for the part of [13] which introduces this indeterminate phenomenon. Namely, we discuss how to obtain associativity in the transcendental calculus and show how the Hadamard finite part procedure can be implemented in our context.

KW - Transcendental calculus

KW - Weyl algebra

UR - http://www.scopus.com/inward/record.url?scp=66249124633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=66249124633&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:66249124633

SN - 9782856292587

T3 - Asterisque

SP - 267

EP - 297

BT - Differential Geometry, Mathematical Physics, Mathematics and Society Part 1

ER -