3
votes
1answer
169 views

Spectral synthesis for central functions on locally compact groups

There is a large literature on harmonic analysis on locally compact group, that I am just beginning to discover. However I have not seen so far anything that emphasizes the central functions on $G$. A ...
11
votes
2answers
735 views

Hopf Algebra for a physicist

Hello, for my bachelor's thesis I need to understand the Hopf Algebra of Feynman Diagrams. As I have only litte knowledge in Algebra by now I wanted to ask where I could start and what preknowledge I ...
7
votes
1answer
300 views

What are the applications of Dowker's theorem?

Let $R \subset X \times Y$ be any relation between sets $X$ and $Y$. CH Dowker constructed two simplicial complexes $K$ and $L$ associated to $R$: a simplex in $K$ consists of finitely many elements ...
4
votes
2answers
371 views

Can we calculate the inner product of a semicontinous function with the Dirac delta function?

Dear all, It is clear that if $f:R\mapsto R$ is a continuous function, than $< f, \delta_x >=f(x)$. Now, if $f$ is only semicontinous, can we say that $< f, \delta_x >=f(x)$? I think this ...
1
vote
1answer
189 views

Order density of smooth functions among continuous functions?

Let $\mathcal{C}^0([a,b],\mathbb{R})$ be the space of all continuous functions $f:[a,b]\rightarrow\mathbb{R}$ and $\mathcal{C}^\infty([a,b],\mathbb{R})$ the subspace of all smooth functions. Define ...
7
votes
4answers
436 views

Trig functions based on convex curves

Pardon my naivety, but I wonder if much use has been found for trigonometric functions defined in terms of a centrally symmetric convex curve $K$ replacing the circle $C$. For example, here is the ...
4
votes
3answers
2k views

n-dimensional “cross product” reference request

I have written a paper which involves a "cross product" in $\mathbb{R}^n$ and I would like to have a reference to point to. Let ${\bf e_1}, \dots, {\bf e_n}$ be the standard basis for $\mathbb{R}^n$ ...
5
votes
1answer
213 views

On the multidimensional generalisation of Gamma function

Gamma function is defined as $$ \Gamma(z) = \int\limits_{0}^{+\infty} x^{z-1} e^{-x} \; dx $$ I'm looking for multidimensional generalisation of this definition. I consider the class $Q$ of ...
1
vote
0answers
207 views

Homotopy-Fibre Sequence of Classifying Spaces

Let $G$ be a topological group and $H$ be a normal subgroup of $G$ (I think $H$ is required to be admissible in the sense that the quotient map $G\to G/H$ is a principal $H$-bundle, am I right?). Then ...
4
votes
3answers
793 views

Computing the q-series of the j-invariant

It is a fundamental fact, often quoted these days in its connection with Monstrous Moonshine, that the q-expansion (i.e., the Laurent expansion in a neighborhood of $\tau = i\infty$) of the ...
2
votes
0answers
602 views

Strong Bezout's Identity?

Let $\{ a_i \}_{i=1}^N $ be a set of elements of the ring of integers, $\mathbb{Z}_D$ and define $g = \text{gcd}(a_1, a_2,\ldots, a_N, D)$. Then Bezout's Identity states that there exists another set ...
14
votes
6answers
4k views

What's the notation for a function restricted to a subset of the codomain?

Suppose I have a function f : A → B between two sets A and B. (The same question applies to group homomorphisms, continuous maps between topological spaces, etc. But for simpicity let's restrict ...
6
votes
1answer
620 views

Inverse function theorem for DC-functions

I would like to have an inverse (or/and) implicite function theorem for DC-functions. It seems that I have right definitions, but I fail to prove it... Definitions: Let $h:\mathbb R^n\to\mathbb R$ ...
5
votes
3answers
385 views

Non-absolute convergence of series with asymtotically equal coefficients

The following seems to be a question related to standard calculus, but I am not quite sure where to look for an answer. Suppose $f,g:\mathbb{N} \to \mathbb{C}$ are such that the have the same ...
11
votes
12answers
4k views

Looking for an introductory textbook on algebraic geometry for an undergraduate lecture course

I am now supposed to organize a tiny lecture course on algebraic geometry for undergraduate students who have interest in this subject. I wonder whether there are some basic algebraic geometry texts ...