Theory of Distribution The set of distribution of order

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 16PPS
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Theory of Distribution
The set of distribution of order <m is denoted by D'm C D. Any distribution
u € D'm for 0 < m < ∞ has a unique extension to a sequentially-continuous
linear functional on C" (R, C). Test functions where convergence of {on} to the
zero function is defined as: the support of all on are contained within a fixed
compact set K and D'n converges uniformly to 0 on K for all 0 < j < m.
Prove that Dm 8o E D' is one of order m. On what class of test functions may
we define the action of 8o?
Transcribed Image Text:Theory of Distribution The set of distribution of order <m is denoted by D'm C D. Any distribution u € D'm for 0 < m < ∞ has a unique extension to a sequentially-continuous linear functional on C" (R, C). Test functions where convergence of {on} to the zero function is defined as: the support of all on are contained within a fixed compact set K and D'n converges uniformly to 0 on K for all 0 < j < m. Prove that Dm 8o E D' is one of order m. On what class of test functions may we define the action of 8o?
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