2:15pm-3:30pm Tuesday and Thursday and (some) Friday 3:00pm - 4:00pm in room 211 MSB.
Also note:
Section Start Date 01/13/2020; Section End Date 04/28/2020; Last Day to Add 01/19/2020; Last Day to Drop 01/19/2020; Last Day to Withdraw 03/22/2020;
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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. 12:30-2:00 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/RV2020.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
|
|
Tuesday (01/14/2020) |
(NO CLASS, NEED TO MAKE UP + Friday) | |
|
Thursday (01/16/2020) |
(NO CLASS, NEED TO MAKE UP + Friday) | |
|
Tuesday (01/21/2020) |
Hilbert space (very quick review) | |
|
Thursday (01/23/2020) |
Hilbert space | |
|
Friday (01/24/2020), 3:00pm - 4:00pm |
Hilbert space + Linear operators | First Homework. |
|
Tuesday (01/28/2020) |
Riesz Theorem represenation Theorem. Adjoin of a linear operator. | |
|
Thursday (01/30/2020) |
An introduction to the Fourier Series | |
|
Friday (01/31/2020), 3:00pm - 4:00pm |
Continuation of Fourier Series | First Homework Due. |
|
Tuesday (02/04/2020) |
Integral Perators & Compact Operators | Second and Third Homeworks. |
|
Thursday (02/06/2020) |
Compact Operators | |
|
Friday (02/07/2020), 3:00pm - 4:00pm |
Compact Operators Pectral Theorem | |
|
Tuesday (02/11/2020) |
(NO CLASS, NEED TO MAKE UP, Friday) | |
|
Thursday (02/13/2020) |
(NO CLASS, NEED TO MAKE UP, Friday) | |
|
Tuesday (02/18/2020) |
(NO CLASS, NEED TO MAKE UP, Friday) | |
|
Thursday (02/20/2020) |
Abstract Measure (Caretheodory measurable) | Second and Third Homeworks due. |
|
Friday (02/21/2020), 3:00pm - 4:00pm |
Abstract Measure (case of the Metric Spaces) | Homework Four |
|
Tuesday (02/25/2020) |
Abstract Measure (Borel Measure) | |
|
Thursday (02/27/2020) |
Abstract Measure (Extension Theorems) | |
|
Friday (02/28/2020), 3:00pm - 4:00pm |
Abstract Measure (Integration) | |
|
Tuesday (03/03/2020) |
Product Measure and Fubini theorem. | Homework Five. Home work 4 is due. |
|
Thursday (03/05/2020) |
Product Measure and Fubini theorem. | |
|
Friday (03/06/2020), 3:00pm - 4:00pm |
Spherical Coordinates and Integration | |
|
Tuesday (03/10/2020) |
Borel Measure on ${\mathbb R}$ and Lebesgue-Stiltjes integral | Home work 5 is due. |
|
Thursday (03/12/2020) |
Reminder for Tuesday lecture (video, and slides). | Homework Six. |
|
Tuesday (03/17/2020) |
Signed measures (video_Direct_Version_KSU, video_google, and slides); | |
|
Thursday (03/19/2020) |
Absolute Continuity of measure (Part 1 video_Direct_Version_KSU and slides); (Part 2 video_Direct_Version_KSU and slides) | |
|
Tuesday (03/24/2020) |
Spring break | |
|
Thursday (03/26/2020) |
Spring break | |
|
Tuesday (03/31/2020) |
Measure Preserving Transformations (video_Direct_Version_KSU, video_google, and slides). | Home work 6 is due. Homework Seven. |
|
Thursday (04/02/20) |
Hilber Space view: Mean ergodic Theorem (video_Direct_Version_KSU, video_google, and slides). | |
|
Tuesday (04/07/2020) |
Maximum Ergodic Theorem. (video_Direct_Version_KSU, video_google, and slides) | Home work 7 is due. Homework Eight. |
|
Thursday (04/09/2020) |
Pointwise Ergodic Theorem (video_Direct_Version_KSU, video_google, and slides) | |
|
Tuesday (04/14/2020) |
Ergodic transormations (video_Direct_Version_KSU, video_google, and slides) | |
|
Thursday (04/16/2020) |
Introduction to $L_p$ spaces: Holder and Minkowski inequalities. (video_Direct_Version_KSU, video_google, and slides) | Home work 8 due. Homework Nine. |
|
Tuesday (04/21/2020) |
$L_p$ space. (video_Direct_Version_KSU, video_google, and slides) | Final Homework. |
|
Thursday (04/23/2020) |
Banach Space. (video_Direct_Version_KSU, video_google, and slides) | |
|
Tuesday (04/28/2020) |
Duality and $L_p$. (video_Direct_Version_KSU, video_google, and slides) | Home work 9 due. |
May 5, 2020 |
FINAL HOME WORK DUE | |