Instructor - J. Iaia
Office - GAB 420
Office phone - 4704
Office hours - MW 11:00-1:00 or by appt.
e-mail - iaia@unt.edu
The University of North Texas makes reasonable academic accommodation for students with disabilities. Students seeking accommodation must first register with the Office of Disability Accommodation (ODA) to verify their eligibility. If a disability is verified, the ODA will provide you with an accommodation letter to be delivered to faculty to begin a private discussion regarding your specific needs in a course. You may request accommodations at any time, however, ODA notices of accommodation should be provided as early as possible in the semester to avoid any delay in implementation. Note that students must obtain a new letter of accommodation for every semester and must meet with each faculty member prior to implementation in each class. For additional information see the Office of Disability Accommodation website at http://www.unt.edu/oda. You may also contact them by phone at 940.565.4323.
Royden, Chapter 7 - 1,4,5,10,13,14,18
1. Show that C[0,1] is a Banach space where ||f|| = sup |f(x)|.
2. Suppose f_n is in L^p[0,1] with 1 < p < infty. Suppose f_n goes to f pointwise a.e. and f is in L^p. Suppose there is an M such that ||f_n|| < M (where || || is the L^p norm). Let g be in L^q where 1/p + 1/q = 1. Show that the integral of f_n g goes to the integral of fg.
3. Let f_n converge to f in L^p[E], 1 <= p < infty, where E is measurable. Let g_n be measurable and suppose there is an M such that |g_n| < M and g_n goes to g a.e. Show that (f_n)(g_n) goes to fg in L^p[E].
Royden, Chapter 17 - 18,21,22,23,25,26,30,33i,ii
Royden, Chapter 18 - 2,3,4,9,12b,23,25,26,45
Royden, Chapter 20 - 2,5,6,9,10,25,26
old qualifying exam questions handed out in class
Last update: August 21, 2002