Functions of Real Variables 1 (62052/72052)

2:15pm-3:30pm Tuesday and Thursday and (some) Friday 3:00pm - 4:00pm in room 211 MSB.

Syllabus.

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;

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

TO ARTEM ZVAVITCH'S HOMEPAGE