Math 7398, section 10532 - Spring 2005

Special topics: Functional Analysis II

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Classes: 1:00-2:30pm MoWe, 350 PGH
Instructor: Andrew Török
Office: 672 PGH
Phone: (713) 743-3478
E-mail: torok@math.uh.edu
Office hours: see the home-page

Assignments

Unless mentioned otherwise, the problems below are from Conway's book.

Section 3.4 denotes chapter 3, section 4.
Exercise 4 in section 1.2 is refered to as E 1.2.4.
Statements from the text (theorems, examples, etc.) are refered to by their number only (e.g., 2.1.3 stands for Example 1.3 in Chapter 2).

Please write the solutions on separate pages (i.e., do not hand in a note-book).

Some of the problems might have the answer or a hint in the textbook. If you have to hand in such a problem, you are welcome to use the hint but have to still write a complete solution.
More difficult problems are marked by a ^*.

HOMEWORKS
HW # Section HAND IN Solve only, do not hand in

1. (due Feb. 9) 4.1 see link 18, 23
4.2 4 (a, c, e, f, h)
[h: for counterexample
can use a Frechet space
defined in this section] 8
2. (due Feb. 16) 4.3 12, see link 14
5.1 8 (hint), 9 (details) 4, 7
5.2 2
5.3 3 (hint) 2 (hint)
5.4 1 2
5.6 2 4 (hint: f: X -> Y cont. induces f: beta X -> beta Y )
5
5.7 9 3, 4, 6
Next problems from Rudin, Functional Analysis
Ch. 6 6(b, c), 7, 8, 10, 12, 14, 24
for f a test function, show that
[x -> translation of f by x] is continuous
from Rⁿ to the space of test functions
prove the claim on line -3 of page 156 (Thm. 6.30):
the partial derivative of a test function is the limit
(in the space of test functions!) of the corresponding quotients.
Ch. 7 1, 3, 4, 5(a), 8, 13

NOTE: please prove all statements, unless they were discussed in class, or are part of the previous homework assignments.

HOMEWORKS
1. (due Feb. 9)	4.1	see link	18, 23
4.2	4 (a, c, e, f, h) [h: for counterexample can use a Frechet space defined in this section]	8
2. (due Feb. 16)	4.3	12, see link	14
5.1	8 (hint), 9 (details)	4, 7
5.2		2
	5.3	3 (hint)	2 (hint)
5.4	1	2
5.6	2	4 (hint: f: X -> Y cont. induces f: beta X -> beta Y ) 5
5.7	9	3, 4, 6
Next problems from Rudin, Functional Analysis
	Ch. 6		6(b, c), 7, 8, 10, 12, 14, 24
	for f a test function, show that [x -> translation of f by x] is continuous from Rⁿ to the space of test functions
	prove the claim on line -3 of page 156 (Thm. 6.30): the partial derivative of a test function is the limit (in the space of test functions!) of the corresponding quotients.
	Ch. 7		1, 3, 4, 5(a), 8, 13

Last modified:

HOMEWORKS
HW #	Section	HAND IN	Solve only, do not hand in
1. (due Feb. 9)	4.1	see link	18, 23
1. (due Feb. 9)	4.2	4 (a, c, e, f, h) [h: for counterexample can use a Frechet space defined in this section]	8
2. (due Feb. 16)	4.3	12, see link	14
	5.1	8 (hint), 9 (details)	4, 7
	5.2		2
	5.3	3 (hint)	2 (hint)
	5.4	1	2
	5.6	2	4 (hint: f: X -> Y cont. induces f: beta X -> beta Y ) 5
	5.7	9	3, 4, 6
Next problems from Rudin, Functional Analysis
	Ch. 6		6(b, c), 7, 8, 10, 12, 14, 24
			for f a test function, show that [x -> translation of f by x] is continuous from Rⁿ to the space of test functions
			prove the claim on line -3 of page 156 (Thm. 6.30): the partial derivative of a test function is the limit (in the space of test functions!) of the corresponding quotients.
	Ch. 7		1, 3, 4, 5(a), 8, 13