01:10pm-2:00pm Monday, Wednesday and Friday in room 211 MSB.
Also note:
Section Start Date 01/17/17; Section End Date 05/07/17; Last Day to Add 01/22/17; Last Day to Drop 01/29/17; Last Day to Withdraw 03/26/17;
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Instructor: Book: Book: Office hours: Office: Office tel.: E-mail: WWW of the course : |
Artem Zvavitch "Real Analysis: Measure Theory, Integration, and Hilbert Spaces" by E. M. Stein, R. Shakarchi. "An Introduction to Measure Theory" by Terrence Tao. 10:30-12:00 TR, but the best is to e-mail me and to make an appointment. 364 (330)-672-33-16 zvavitch@math.kent.edu http://www.math.kent.edu/~zvavitch/RV2016.html |
Please, note the calendar below is just a plan. Homework and Exams dates may be adjusted during the semester!
|
Date
|
Lecture Topic
|
Special Remarks
|
|
Wednesday (01/18/17) |
Hilbert space (very quick review) | First Homework. |
|
Friday (01/20/17) |
Hilbert space (very quick review) + Linear operators | |
|
Monday (01/23/17) |
Riesz Theorem represenation Theorem. Adjoin of a linear operator. | |
|
Wednesday (01/25/17) |
Examples, Examples and Examples. | Second Homework. First Homework Due. |
|
Friday (01/27/17):
REGULAR TIME + 3:15-4:05 |
Compact Operators. | |
|
Monday (01/30/17) |
Compact Operators | |
|
Wednesday (02/01/17) |
Spectral Theorem | Third Homework. Second Homework Due. |
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Friday (02/03/17):
REGULAR TIME + 3:15-4:05 |
Back to Measure! | |
|
Monday (02/06/17) |
Exterior Measure and Caratheodory theorem. | |
|
Wednesday (02/08/17) |
Metric spaces. Borel $\sigma$-algebra. | Fourth Homework. Third Homework Due. |
|
Friday (2/10/17) |
Exterior Measure on a Metric Space. | |
|
Monday (02/13/17) |
Exterior Measure on a Metric Space. Borel measure. | |
|
Wednesday (02/15/17) |
NO CLASS, NEED TO RESCHEDULE | |
|
Friday (02/17/17) |
NO CLASS, NEED TO RESCHEDULE | |
|
Monday (02/20/17) |
Extension Theorem. | Fourth Homework due |
|
Wednesday (02/22/17) |
Extension Theorem. | Fifth Homework. |
|
Friday (02/24/17) |
Measurable functions and integration. | |
|
Monday (02/27/17) |
Product measure and general Fubini Theorem. | |
|
Wednesday (03/01/17) |
NO CLASS, NEED TO RESCHEDULE | |
|
Friday (03/03/17): REGULAR TIME + 3:15-4:05 |
Fubini Theorem. Integration in Polar coordinates (example) | Fifth HW is due. Sixt Homework. |
|
Monday (03/06/17) |
Integration in Polar coordinates (proof) | |
|
Wednesday (03/08/17) |
Borel measure on R and the Lebesgue-Stieltjes integral. | |
|
Friday (03/10/17) |
Borel measure on R and the Lebesgue-Stieltjes integral. | Sixt HW due. |
|
Monday (03/13/17) |
Absolute Continuity of measures: signed measures.) | Homework Seven |
|
Wednesday (03/15/17) |
No class, weather | |
|
Friday (03/17/17) |
Absolute Continuity. | |
|
Monday (03/20/17) |
Decomposion of measure (Radon - Nikodym theorem). | Sevens HW due. Homework Eght |
|
Wednesday (03/22/17) |
Absolute Continuity (Radon - Nikodym theorem). | |
|
Friday (03/24/17) REGULAR TIME + 3:15-4:05 |
Ergodic Theorems and Measure-preserving transormations. | |
|
Monday (03/27/17) |
NO CLASS, SPRING BRAKE | |
|
Wednesday (03/39/17) |
NO CLASS, SPRING BRAKE | |
|
Friday (03/31/17) |
NO CLASS, SPRING BRAKE | |
|
Monday (04/03/17) |
Ergodic Theorems | . |
|
Wednesday (04/05/17) |
Ergodic Theorems | |
|
Friday (04/07/17) |
Ergodic Theorems | |
|
Monday (04/10/17) |
Ergodic maps and applications. | |
|
Wednesday (04/12/17) |
Ergodic maps and applications. | |
|
Friday (04/14/17) REGULAR TIME + 3:15-4:05 |
Welcome to $L_p$ space. | Home Work Eight is due |
|
Monday (04/17/17) |
$L_p$-spaces. | |
|
Wednesday (04/19/17) |
$L_p$-spaces | Homeworks Nine and Ten |
|
Friday (04/21/17) |
$L_p$-spaces | |
|
Monday (04/24/17) |
No class | |
|
Wednesday (04/26/17) |
$L_p$-spaces. Banach Spaces. | |
|
Friday (04/28/17) |
Banach Spaces Examples and Linear Functionals | Homeworks Nine and Ten due. |
|
Monday (05/01/17) |
Duality | Final Home Work |
|
Wednesday (05/03/17) |
$L_p$ and duaity. | |
|
Friday (05/05/17) |
No class | |
|
May 14 |
FINAL HOME WORK DUE (over email) | |