# Questions tagged [regularization]

The tag has no usage guidance.

64 questions
Filter by
Sorted by
Tagged with
53 views

283 views

### A proposition for summing divergent series, but how should partial summation be defined at non-natural values?

Introduction I have been in search of methods of assinging values to divergent series that have a nice intuitive or geometric interpretation. One fairly straightforward method I've considered for ...
740 views

### Divergent series summation beyond natural boundaries

I'm hoping to investigate the effects of divergent summation methods on series which cannot be analytically continued due to a dense set of singularities. At least a priori, it doesn't seem that a ...
1k views

### Value of divergent sum $\sum_{n=0}^\infty (-1)^n n^n$

I'm hoping to find a reasonable value to assign to the divergent series $\sum_{n=0}^\infty (-1)^n n^n$ and $\sum_{n=0}^\infty (-1)^n (xn)^n$. For the first one, I have obtained something around 0.71, ...
207 views

### Hypermodulus and what mathematical objects have it

When researching divergent integrals, I decided to introduce a concept of "modulus" or "determinant" of divergent integral (and series). Basically, it is the exponent of the real ...
70 views

### Improving regularity of the boundary of a convex set in Riemannian manifolds

Let $X$ be a geodesically complete Riemannian manifold (we may assume that $X$ is simply connected and negatively curved, although I don't think it matters). Given a closed, convex subset $K \subset X$...
1 vote
203 views

190 views

### Generalised limits via derivatives of integrals?

Assuming that $f$ is a continuous function, we have that $$f(x) = \frac{d}{dx}\int f(t)\,dt.$$ Assuming instead that $f$ has a removable singularity at $x=a$, and is otherwise continuous, we have ...
688 views

### Regularizing the sum of all primes

In the spirit of a similar question for the harmonic series, is there a way to regularize the (divergent) sum of all primes? $$\sum_{p \text{ prime}} p$$ Neither of these questions obtained a ...
729 views

1 vote
45 views

1 vote
239 views

### Significance of Tikhonov matrix

I am looking for a tutorial on Tikhonov matrix, in the sense what it can do or it cannot do. The definition of the matrix can be obtained in the wikipedia link. https://en.wikipedia.org/wiki/...
It seems natural to consider $\lim_{q \rightarrow 1^-} \sum_{n \in S} q^n - \sum_{n \in T} q^n$, when it exists, as a way of comparing the sizes of two sets $S,T \subseteq {\bf N}$ that have the same ...
I have a $C^{1,\alpha}$ surface defined as the graph of some function $\varphi : B \to \Bbb{R}_+$ ($B$ is a ball). This surface has positive and bounded mean curvature in the weak sense (since the ...