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Topology and Analysis

- Point-set topology. Real, complex, harmonic and functional analysis. Measure and integration theory
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
1 28,513
hi there, I am trying to prove the following inequality: let z\in \mathbb{D} then \left| \frac{z}{\lambda}...
T 04:08 PM
1 63
I know this post is in the topology thread of this forum, for group theory, this seemed like the reasonable choice to...
T 02:56 PM
0 65
Say we have two functions with the following properties: f(x) is negative and monotonically approaches zero as x...
T 10:59 AM
2 95
Hi all, Please help! I am reading the paper "A note on contiguity and Hellinger distance" by J. Oosterhoff and W.R....
T 12:13 AM
2 99
Hi all, I am trying to construct a continuous matrix-valued function h=h(f,g) ; f,g in C^1,all defined in an open...
Aug14-14 10:35 PM
4 464
Recently I came across this information: \text{S1} = 1+1+1+1+\dotsb= -\frac{1}{2} \text{S2} = 1-1+1-1+\dotsb=...
Aug13-14 03:32 PM
1 136
We know that the derivative of the general Schwartz - Christoffel map (function) is: f'(z) = λ(z -...
Aug13-14 11:19 AM
2 1,278
Hello. I'm wondering if anyone has a table of transforms showing the result of an Abel transform on a Gaussian...
Aug11-14 10:45 AM
Mr Boom
1 186
Just as we have orthogonal vectors/vector spaces/etc., we can have orthogonal functions/function spaces/etc. I'm...
Aug10-14 09:45 PM
17 348
The Problem Let x and y be real numbers such that y<x, using the Dedekind cut construction of reals prove that...
Aug9-14 06:40 PM
5 238
I'm trying to understand Čech cohomology and for this I'm looking at the example of ##S^1## defined as ##/\sim## with...
Aug7-14 12:05 AM
2 1,489
I am trying to reconcile the following statement: " ||u||<=eps*||f|| means ||u||=O(eps) ("||u|| is order eps")... "...
Aug4-14 11:58 PM
Simon Bridge
7 219
Consider the sets ##X:= \{x\in\mathbb R^2: \enspace ||x-(-1,0)||_2 \leq 1\}## (a ball) and ##Y:=co\{(0,-1), (0,1),...
Aug4-14 10:34 PM
2 123
Are plane and surface of sphere different metric spaces? Can distance function of plane be applied as distance...
Aug2-14 09:00 PM
6 268
I'm interested in topology/differential geometry and before I eventually graduate I am looking to complete an...
Aug2-14 06:50 PM
5 222
Just as the title says, what is a POD? I've tried reading papers but I feel I am missing something. Does anyone have a...
Jul28-14 01:16 PM
5 1,259
I am trying to show that for f in C , and ##n=0,1,2,... ## we have: ## \int_0^1 x^n f(x)dx =0 ## (&&) , then...
Jul19-14 03:26 AM
4 610
Hi All, This is a follow-up to another post. Question is: Is the restriction of an isotopy that is the identity...
Jul19-14 03:23 AM
6 757
Hi all, Isn't the mapping class group of a contractible space trivial (or, if we consider isotopy, {+/-Id})? ...
Jul15-14 08:30 PM
11 2,231
I've been reading Thomas Jordan's Linear Operators for Quantum Mechanics, and I am stalled out at the bottom of page...
Jul13-14 04:05 PM
2 1,351
I was suprised to realize that foliation theory was actually closely related to topology. Indeed,...
Jul12-14 08:28 PM
2 1,875
Suppose, for a suitable class of real-valued test functions T(\mathbb{R}^n), that \{G_x\} is a one-parameter family of...
Jul10-14 04:32 PM
Greg Bernhardt
1 2,566
How to calculate ##\int^{\infty}_{-\infty}\frac{\delta(x-x')}{x-x'}dx'## What is a value of this integral? In some...
Jul6-14 04:49 PM
14 4,554
I don't have the whole book A First Course in Sobolev Spaces by G. Leoni myself, but I have obtained a pdf file of the...
Jul6-14 12:00 AM
3 1,364
Visualizing a higher-dimensional sphere seems impossible to me. The best that can be done is to come up with several...
Jul3-14 09:17 AM
2 3,440
Hello! My problem consists of : there is a representation of an uneven surface in terms of Fourier series with...
Jul2-14 03:33 PM
2 2,006
This question is in this rubric because I figured it belonged to measure theory, but I am ready to move it if I am...
Jul2-14 11:13 AM
2 1,693
Suppose we are given two functions: f:\mathbb R \times \mathbb C \rightarrow\mathbb C g:\mathbb R \times \mathbb C...
Jun13-14 04:38 PM
1 1,620
Hi all, Could you please help me understand the Fresnel integral and Green's functions? Could you please explain...
Jun13-14 06:15 AM
2 1,434
series expansion: ln(1+x)=1-x^2/2+x^3/3-x^4/4+x^5/5+..........................∞ ...
Jun12-14 12:17 PM
12 1,735
Hello everyone,i am doing my project in image processing.... i have done video sementation using the Fourier...
Jun11-14 05:42 AM
2 1,557
Could anybody explain what divisors and the Riemann-Roch theorem are intuitively, motivating them, without any jargon...
Jun10-14 12:31 AM
3 1,502
Assumptions: f:\to\mathbb{R} is some measurable function, and M is some constant. We assume that the function has the...
Jun8-14 04:27 PM
10 2,400
I want to show that the modulus of the automorphism \frac{a-z}{1-\overline{a}z} is strictly bounded by 1 in the...
Jun5-14 05:20 PM
2 1,415
hey pf! physically, what does a fourier transform do? physically what comes out if i put velocity in? thanks! ...
Jun5-14 12:36 AM
Simon Bridge
18 3,474
Hello One problem I often think I have is that I am able to solve a problem, but not really understanding the idea...
Jun4-14 01:57 PM
4 1,706
Is it possible for a ball(with nonzero radius) to be empty in an arbitrary metric space?
Jun2-14 12:39 PM
1 1,493
Is it possible to perform a Fourier transform on a shape instead of a rectangular region? To be specific I am...
May30-14 04:49 AM
1 1,477
Can someone tell me if the continuous fourier transform of a continuous (and vanishing fast enough ) function is also...
May28-14 02:29 AM
4 1,548
Can anybody helps in suggesting books on Fourier transforms and applications. I have seen many applications of Fourier...
May26-14 07:48 PM
8 1,870

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