Lecture Notes, Exercises etc
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Notes and exercises for graduate and undergraduate studentsSun, 27 May 2018 11:42:17 +0000enhourly1http://wordpress.com/https://s0.wp.com/i/buttonw-com.pngLecture Notes, Exercises etc
https://statmathbc.wordpress.com
An exercise in Calculus
https://statmathbc.wordpress.com/2018/05/08/an-exercise-in-calculus-2/
https://statmathbc.wordpress.com/2018/05/08/an-exercise-in-calculus-2/#respondTue, 08 May 2018 10:27:32 +0000http://statmathbc.wordpress.com/?p=803Let f be infinitely differentiable. Suppose $|f(x)| \leq c_n |x|^{n}$ in some neighborhood of 0, for each n. Show that $f^{(n)} (0)=0$ for all n.
]]>https://statmathbc.wordpress.com/2018/05/08/an-exercise-in-calculus-2/feed/0statmathbcAn exercise on bounded sequences of monotone functions
https://statmathbc.wordpress.com/2018/04/06/an-exercise-on-bounded-sequences-of-monotone-functions/
https://statmathbc.wordpress.com/2018/04/06/an-exercise-on-bounded-sequences-of-monotone-functions/#respondFri, 06 Apr 2018 08:56:52 +0000http://statmathbc.wordpress.com/?p=801Show that any uniformly bounded sequence of monotonically increasing functions has a subsequence converging at every point
]]>https://statmathbc.wordpress.com/2018/04/06/an-exercise-on-bounded-sequences-of-monotone-functions/feed/0statmathbcCatalog
https://statmathbc.wordpress.com/2018/04/06/november-2017-catalog/
https://statmathbc.wordpress.com/2018/04/06/november-2017-catalog/#respondFri, 06 Apr 2018 08:46:58 +0000http://statmathbc.wordpress.com/?p=655Catalog of notes available here (updated monthly) I have not included the problems I post occasionally. Thanks to Nishant and Tiju for suggestions. A few links do not work. Please use the search feature on the site for these.
For hints/solutions to exercises as well as for comments/suggestions send mail to kavi.ramamurthy@gmail.com
1. Banach – Stone Theorem
2. Basic Wavelet Theory
3. Brunn – Minkowsky Inequality
4. Caratheodory Extension Theorem
5. Compactness in Metric Spaces
6. Continuous Hilbert Transform
7. Fourier Analysis on Groups
8. Fourier Series and Fourier Transforms
9. Gelfand – Naimark Theorem
10. Infinitely Divisible and Stable Laws Vol. 1
11. Infinitely Divisible and Stable Measures V. II
12. Laurent Schwartz’ Theory of Distributions
13. Marcinkiewicz Interpolation Theorem
14. Mergelyan’s Approximation Theorem
15. Notes on Fixed Point Theorems
16. Notes on Functional Analysis
17. Notes on Rado’s Theorem
18. The Stone – Weierstrass Theorem
19. Wiener’s Tauberian Theorem
20. Infinitely Divisible and Stable Measures V. III (Type and Cotype)
21. Exercises in Probability Theory
22. Exercises in Analysis 1-100
23. Exercises in Analysis – 101 to 200
24. Exercises in Analysis – 201 to 300
25. Exercises in Analysis – 301 to 400
26. Notes on Ergodic Theory
27. The Banach Stone Theorem
28. “Anti-Calculus Proposition” of Erdos
29. Exercises in Analysis – 401 to 500
30. Exercises in Analysis 501-600
31. Exercises in Analysis 601-700
32. Exercises in Complex Analysis 1-100
33. Exercises in Complex Analysis 101-200
34. Exercises in Complex Analysis 200-
]]>https://statmathbc.wordpress.com/2018/04/06/november-2017-catalog/feed/0statmathbcExercises in Analysis 1-100
https://statmathbc.wordpress.com/2018/03/19/exercises-in-analysis-1-100/
https://statmathbc.wordpress.com/2018/03/19/exercises-in-analysis-1-100/#respondMon, 19 Mar 2018 09:09:13 +0000http://statmathbc.wordpress.com/?p=7971to100RA
]]>https://statmathbc.wordpress.com/2018/03/19/exercises-in-analysis-1-100/feed/0statmathbcExercises in Complex Analysis 200-270
https://statmathbc.wordpress.com/2018/02/22/exercises-in-complex-analysis-200-270/
https://statmathbc.wordpress.com/2018/02/22/exercises-in-complex-analysis-200-270/#respondThu, 22 Feb 2018 09:58:43 +0000http://statmathbc.wordpress.com/?p=791CAP
]]>https://statmathbc.wordpress.com/2018/02/22/exercises-in-complex-analysis-200-270/feed/0statmathbcAn exercise on i.i.d. sequences
https://statmathbc.wordpress.com/2018/02/16/an-exercise-on-i-i-d-sequences/
https://statmathbc.wordpress.com/2018/02/16/an-exercise-on-i-i-d-sequences/#respondFri, 16 Feb 2018 09:32:32 +0000http://statmathbc.wordpress.com/?p=784Let {X_n} be an i.i.d sequence and assume that X_1 is not a bounded random variable. Show that there is a sequence of continuous functions {f_n} on the real line converging uniformly to 0 on compact subsets such that $\latex P{f_n(X_n) \to 0}=0$.
]]>https://statmathbc.wordpress.com/2018/02/16/an-exercise-on-i-i-d-sequences/feed/0statmathbcExercises in Complex Analysis 101-200
https://statmathbc.wordpress.com/2018/02/05/exercises-in-complex-analysis-101-200/
https://statmathbc.wordpress.com/2018/02/05/exercises-in-complex-analysis-101-200/#respondMon, 05 Feb 2018 09:40:43 +0000http://statmathbc.wordpress.com/?p=780CA101200
]]>https://statmathbc.wordpress.com/2018/02/05/exercises-in-complex-analysis-101-200/feed/0statmathbcAn exercise involving a functional equation
https://statmathbc.wordpress.com/2018/01/29/an-exercise-involving-a-functional-equation/
https://statmathbc.wordpress.com/2018/01/29/an-exercise-involving-a-functional-equation/#respondMon, 29 Jan 2018 09:07:03 +0000http://statmathbc.wordpress.com/?p=776Let f be a function from R to R such that f(x+y^{n})=f(x)+{f(y)}^{n} for all x,y where n is a given positive integer greater than 1. Show that f(x)=cx where either c=0 it c is an n-th root of unity.
No hypothesis on continuity or measurability of f!
]]>https://statmathbc.wordpress.com/2018/01/29/an-exercise-involving-a-functional-equation/feed/0statmathbcSolution to a problem posted on S-E
https://statmathbc.wordpress.com/2018/01/24/solution-to-a-problem-posted-on-s-e/
https://statmathbc.wordpress.com/2018/01/24/solution-to-a-problem-posted-on-s-e/#respondTue, 23 Jan 2018 22:43:29 +0000http://statmathbc.wordpress.com/?p=773Solution
]]>https://statmathbc.wordpress.com/2018/01/24/solution-to-a-problem-posted-on-s-e/feed/0statmathbcExercises in Complex Analysis 1-100
https://statmathbc.wordpress.com/2018/01/03/exercises-in-complex-analysis-1-100/
https://statmathbc.wordpress.com/2018/01/03/exercises-in-complex-analysis-1-100/#respondWed, 03 Jan 2018 09:49:17 +0000http://statmathbc.wordpress.com/?p=767CA12200
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