Changes of variables in hypersingular integrals
We prove that if A is a nonsingular nxn matrix and ø is smooth for x≠0, integrable outside of a ball, and at the origin it has an asymptotic expansion of the type ø (x) ~ ∑j=0 ∞ aj (x/x) raj as r = |x| → 0, where a,j?V (S) and αj ↗∞,αi = -n, then the hypersingular integral F.p. ∫Rn ø(Ax) dx is given as. We apply this find similar formulas to obtain the transformation rules for linear changes of variables in pseudofunctions, Pf(Axβ), if A is a nonsingular nxn matrix.
Publication Source (Journal or Book title)
Indian Journal of Mathematics
Estrada, R. (2018). Changes of variables in hypersingular integrals. Indian Journal of Mathematics, 60 (1), 23-36. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/267