Periodic Delta Function and Poisson Integral for - Gauge-institute.org

Gauge Institute JournalH. Vic DannonBy 8.4,δ ( ξ − x) = P ( ξ − x). Thus,Periodicoissonξ=1dr(2 − dr)f ( x) = ∫ f( ξ) 2(1 −dr )(1 − cos πξ [ − x ]) + ( dr )ξ=−112 2d ξ=ξ=1∫ξ=−1f211 − r() ξ2 12+ r − 2 r cos πξ ( −x)r =− 1 drdξ= P S {()} f x .oissonIn particular, the Periodic Delta Functionviolates the Poisson Conditions The Hyper-realδ( x), is not defined in the Calculus of Limits,andδ ( x)is not integrable in any bounded interval.1(2δ( x + 0) + δ( x − 0) ) = 0 does not replace δ( x)at itsdiscontinuity point, x = 0 .But by 9.2,Periodic( x )satisfies the Poisson Integral Theorem.δ36