All Questions
7 questions
8
votes
0
answers
304
views
On the remainder of a power series evaluated on the boundary of its convergence disk
Background
This question is related to this one, in the sense that, as the previous one, it originates from my efforts to extend an estimate on the remainder of a power series on a non necessarily ...
- 6,357
7
votes
1
answer
488
views
On a paper by Dimitrie Pompéiu and on one (in two parts) by Edmund Landau
To celebrate the new year and the future of mathematics (or the mathematics of future), I see no better way to ask a question stemming from my researches on power series.
The two papers the title ...
- 6,357
6
votes
1
answer
290
views
Analytic maps on Banach spaces: analyticity upgrade
Consider the following problem.
Let $E,F,G$ be real or complex Banach spaces, such that $F\subset G$ with continuous embedding. Let $U\subset E$ an open set and
$$ f:U\to G $$
an analytic map, such ...
- 1,065
3
votes
0
answers
120
views
On tangential approach regions for general power series converging on the unit disk
Notation and premises. Here it is a list of notations more or less explicitly used in the question:
If $z\in\Bbb C$ then $z = re(t)$ where $r\in \Bbb R_{\ge 0}$, $t\in [0,1]$ and $e(t)\triangleq \exp(...
- 6,357
2
votes
0
answers
320
views
Solution to algebraic equations over $\mathbb{C}$ and $\mathbb{C}[x]$
$t^n=a$, we get one solution to the equation:
$$t=e^{\frac{1}{n}\int^a_1 \frac{1}{x}}$$ generalizing this result by replacing the exponential with an elliptic modular function and the integral with ...
- 3,084
0
votes
1
answer
163
views
Reference(s) on the smallest concave majorant for the sequence of coefficients of a given power series?
This question is based on this Math.SE answer, so let's recall a few concepts dealt with there. If $\{a_n\}_{n\in\Bbb N}$ is the sequence of coefficients of a power series $\sum_{n=0}^\infty a_nz^n$ ...
- 6,357
0
votes
0
answers
332
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 better,...
- 3,084