# home4 - MATH 7338 HOMEWORK#4 Due date December 3 2009 Work...

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Unformatted text preview: MATH 7338 HOMEWORK #4 Due date: December 3, 2009 Work FOUR of the following problems and hand in your solutions. You may work together with other people in the class, but you must each write up your solutions independently. A subset of these will be selected for grading. Write LEGIBLY on the FRONT side of the page only, and STAPLE your pages together. Definition 1. If μ is a continuous linear functional on C ∞ c ( R ) and there exists a single integer N ≥ 0 such that for each compact K ⊆ R there is a constant C K > 0 such that |( f, μ )| ≤ C K N summationdisplay n =0 bardbl f ( n ) bardbl ∞ , f ∈ C ∞ ( K ) , (1) then we say that μ has finite order . In this case, the order of μ is the smallest integer N ≥ such that we can find C K > 0 so that equation (1) holds for every compact K ⊆ R . If no such N exists, then the order of μ is ∞ . Definition 2. If μ ∈ D ′ ( R ) and θ ∈ C ∞ ( R ), then θμ : C ∞ c ( R ) → C is given by (big f, θμ )big = (big f...
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home4 - MATH 7338 HOMEWORK#4 Due date December 3 2009 Work...

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