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## FunctionalAnalysis

by: Moshe Swift III

34

0

1

# FunctionalAnalysis MATH640

Moshe Swift III
Drexel
GPA 3.63

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Moshe Swift III on Wednesday September 23, 2015. The Class Notes belongs to MATH640 at Drexel University taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/212301/math640-drexel-university in Mathematics (M) at Drexel University.

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Date Created: 09/23/15
WA 2 April 8 2009 Submit your solutions on Tuesday April 14 1 2 pt Problem 111 the case lal lt1 Hint Use an argument similar to the one in Example 116 2 an extra credit problem7 1 pt Problem 111 the case lal gt 1 Hint Use the Cauchinoursat theorem from Complex Analysis 3 2 pts Problem 23 4 an extra credit problem7 2 pts Problem 26 Hint You might nd useful the fact that if a sequence of functions converges in the supremumnorm then it converges to the same limit function in the norm induced by the inner product prove it if you use it 5 2 pts Problem 214 Hint In order to prove that the subspace RH2 is closed in RL2 it suf ces to show that for any sequence of functions fn 6 RH2 which converges in RL27 the limit function f belongs to RHQ Let be such a convergent sequence7 and let the limit function which is rational by the de nition of RL2 be represented as where 102 and 972 are co prime polynomials ie7 they have no common zeros Step 1 Show that fnq 6 RH2 for n 12 p E RH27 and fnq A p in RH2 as n A 00 Step 2 Use the Szego reproducing kernel 16042 see Problem 111 to show that for any a E D fn01qagt pa as n A Step 3 Use the result of Step 2 to show that 4a 0 for any a 6 ll Step 4 Conclude from Step 3 that f E RHQ 6 2 pts Problem 32 Hint Follow the outline that was given in class 7 2 pts Show that C0l7 is a Banach space

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