0
votes
0answers
66 views

Examples of functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition

there are examples of lacunary functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition.I want to know more examples of those functions,the more the ...
7
votes
6answers
381 views

Do you have examples of such “transitive” elements?

(I've asked the same question at the MSE, so far with no answers, so I thought I'd try it here as well. If there's some clash with any site rules, please let me know and I'll abide.) Let $A$ be a set ...
0
votes
1answer
191 views

Examples of groups such that order isomorphism of the subgroups of $G\times G$ and $H\times H$ does not imply isomorphism of $G$ and $H$

Let $G$ and $H$ be groups, $\operatorname{Sub}(G\times G)$ be the set of all subgroups of $G\times G$ and $\operatorname{Sub}(H\times H)$ be the set of all subgroups of $H\times H$. Assume there ...
13
votes
1answer
809 views

Learning a little Motivic Cohomology

Simply because I find it interesting, I have spent some time studying motivic cohomology from the lectures by Mazza, Voevodsky and Weibel. However, I'm finding it hard to tell if the theory is ...
9
votes
2answers
410 views

Has there been any application of tensor species?

Joyal's combinatorial species, endofunctors in the category of finite sets with bijections $\mathbf B$ have found numerous applications. One generalisation is given by so-called "tensor species" ...
2
votes
2answers
589 views

Non-split groups

I am looking for a reference with definitions on what it means for an algebraic group to be split, quasi-split, and non-split. I would like to see some examples of the different "types". Thanks, Tom
2
votes
2answers
396 views

description of functions of conditionally negative type on a group

Recall that a kernel conditionaly of negative type on a set $X$ is a map $\psi:X\times X\rightarrow\mathbb{R}$ with the following properties: 1) $\psi(x,x)=0$ 2) $\psi(y,x)=\psi(x,y)$ 3) for any ...
24
votes
12answers
4k views

Explicit computations using the Haar measure

This question is somewhat related to my previous one on Grassmanians. The few times I've encountered the Haar measure in the course of my mathematical education, it's always been used in a very ...
14
votes
1answer
768 views

Comodule exercises desired

This Question is inspired by a Quote of Moore's "There are two ‘evil’ influences at work here: 1. we are toilet trained with algebras not coalgebras 2. some of us are addicted to manifolds and so ...
3
votes
3answers
1k views

Examples of Banach spaces and their duals

There are many representation theorems which state that the dual space of a Banach space $X$ has a particularly concrete form. For example, if $X = C([0,1],\mathbb R)$ is the space of real-valued ...
2
votes
4answers
718 views

Examples of divisors on an analytical manifold

I am trying to understand divisors reading through Griffith and Harris but it is difficult to come up with any particular interesting example. I have browsed through Hartshone's book but everything is ...