Recurrence formulas between Pm and the k-th derivative of Dirac delta supported on P
DOI:
https://doi.org/10.5377/nexo.v22i2.46Keywords:
Recurrence, singular potentialsAbstract
In this paper we gave a sense to recurrence formula Pm .δ (k) (P) -Cm, kδ (k-m) (P) = 0 if k ≥ m (see formula 15) considering the condition gradP ≠ 0, where the constant Cm,k was defined by formula 16. In the second paragraph we gave a sense to the same formua for the special case P = P(x) = P(x1, ...xn) = x12 + x22 + ...xp2 - xp+12 - ...xp+q2.
Our formula is a generalization of the Gelfand and Shilov formula (c.f. ([1]), page 233) and is considered for example, by Bollini, Giambiagi and Tiomno for their theory of analytic regularization in classical Yang-Mills equations and its applications for the singular potentials (c.f. [4]).
Keywords: Recurrence; singular potentials
DOI: 10.5377/nexo.v22i2.46
Nexo Revista Científica Vol. 22, No. 02, pp.72-79/Diciembre 2009
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