h5color - ECE 580 / Math 587 SPRING 2011 Correspondence #...

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Unformatted text preview: ECE 580 / Math 587 SPRING 2011 Correspondence # 14 March 30, 2011 ASSIGNMENT 5 Reading Assignment: Text: Chapter 5, Sections 1-9 Advance Reading: Text: Chapter 5, Sections 10-13. Recommended Reading: Curtain & Pritchard: pp. 65-67, and Chapter 12; Balakrishnan: pp. 62-80, and Chapter 2. Problems (to be handed in): Due Date: Tuesday, April 12 . 34. Let X = C [0 , 1] with the standard maximum norm, and f X * be defined by f ( x ) = x (1 / 4) + 3 x (1 / 2) + 2 1 tx ( t ) dt i) Compute f , the norm of f . ii) Obtain a function of bounded variation on [0 , 1], say v ( ), such that v (0) = 0 and f ( x ) = 1 x ( t ) dv ( t ) 35. Let g 1 , g 2 , . . . , g n be linearly independent linear functionals on a vector space X . Let f be another linear functional on X such that for every x X satisfying g i ( x ) = 0 , i = 1 , 2 , . . . , n , we have f ( x ) = 0. Show that there exist constants 1 , 2 , . . . , n such that f = n i =1 i g i ....
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This note was uploaded on 10/11/2011 for the course ECE 580 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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h5color - ECE 580 / Math 587 SPRING 2011 Correspondence #...

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