On the Noncommutative Neutrix Product of Distributions
نویسندگان
چکیده
Let f and g be distributions and let gn = (g ∗ δn)(x), where δn(x) is a certain sequence converging to the Dirac-delta function δ(x). The noncommutative neutrix product f ◦ g of f and g is defined to be the neutrix limit of the sequence { f gn}, provided the limit h exists in the sense that N-limn→∞〈 f (x)gn(x),φ(x)〉 = 〈h(x),φ(x)〉, for all test functions in . In this paper, using the concept of the neutrix limit due to van der Corput (1960), the noncommutative neutrix products xr + lnx+ ◦ x−r−1 − lnx− and x−r−1 − lnx− ◦ xr + lnx+ are proved to exist and are evaluated for r = 1,2, . . . . It is consequently seen that these two products are in fact equal.
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