Math 891
Graduate Core Course in Analysis I
Fall 2009
Instructor
Roland Speicher
Office: Jeffery Hall, Room 506
Telephone: 533-2388
E-mail: speicher@mast.queensu.ca
Office hour: Wednesday, 2-3pm
Times and Place
The lectures are in Jeffery Hall, Room 422
Monday, 1-2:30 pm
Wednesday, 11:30-1pm
Announcements
The final exam will take place on Tuesday, December 8, from 9am - 12 noon, in
Jeffery 422.
Presentations
Schedule of Presentation
Thursday, Nov. 5, room 202
Matthew Lewis: 10:30
Hu Jiaxiong: 11:00
Thursday, Nov. 12, room 202
Nathan Grieve: 10:30
Martin Helmer: 11:00
Manuel Gil: 11:30
Thursday, Nov. 19, room 202
Carlos Vargas: 10:30
Octavio Arizmendi: 11:00
Charlotte Haley: 11:30
Caroline Seguin: 12:00
Thursday, Nov. 26, room 202
Chris Vanni: 10:30
Andrew Harder: 11:00
Thursday, Dec. 3, room 202
Adam McCabe: 11:30
Topics
All references with the exception of the last topic are to the book of
Rudin: Real and Complex Analysis
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Chapter II: Positive Borel Measures
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Urysohn's Lemma (2.12 in Rudin): Matthew Lewis
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Lusin's Theorem (2.24 in Rudin): Hu Jiaxiong
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Vitali-Caratheodory Theorem (2.25 in Rudin)
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Chapter VIII: Integration on product spaces
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Completion of product measures (Theorem 8.12 and Lemma 1 and 2):
Nathan Grieve
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Convolutions (Theorem 8.14): Martin Helmer
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Chapter III: Lp-spaces
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Jensen's inequality (Theorems 3.2 and 3.3): Manuel Gil
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Chapter IV and V: Hilbert and Banach spaces
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Fourier series in L^2 (4.26 in Rudin): Carlos Vargas
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Banach-Steinhaus Theorem (Theorem 5.8): Octavio Arizmendi
Echebaray
-
Fourier series of continuous functions (5.11 in Rudin): Charlotte
Haley
-
Fourier coefficients of L^1-functions (5.14 and Theorem 5.15):
Caroline Seguin
-
Chapter VI: Complex Measures
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Total variaton of a complex measure (Theorems 6.2 and 6.4 and Lemma
6.3): Chris Vanni
-
Hahn Decomposition of real measure (Theorems 6.12 and 6.14):
Andrew Harder
-
Unbounded Operators (Chapter 13 from Rudin: Functional analysis)
-
Definition of unbounded operator and its adjoint, symmetric and
selfadjoint operator
(13.1, 13.2, 13.3, maybe also 13.4 from Rudin:
Functional Analysis): Adam McCabe
Assignements
Assignment 1 (due September 28, in class)
(Note that there was a small typo in Question (2c). This has now been
corrected.)
Assignment 2 (due October 14, in class)
Assignment 3 (due October 28, in class)
Assignment 4 (due November 11, in class)
Assignment 5 (due November 30, in class)
Topics of Course
We will cover most of the first half of Rudin; mostly
measure and integration theory, and the basics of Hilbert space
and Banach space theory
Text Materials
The following book is recommended for the course:
Rudin: Real and Complex Analysis. Third Edition
(This book will also be used for Math 892.)
Other useful books are:
Conway: A Course in Functional Analysis
Royden: Real Analysis
Pedersen: Analysis Now
Halmos: Measure Theory
Marking Scheme
Assignments: 30%
Presentations: 30%
Final Exam: 40%
One needs at least 50% in the Final Exam to pass the Course.
The presentations will consist of preparing (in written form)
and delivering a talk of about 20 minutes on a topic related to the
course. Possible topics will be posted later.