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pro vyhledávání: '"O’Farrell, A. G."'
Given $n$ buttons and $n$ bulbs so that the $i$th button toggles the $i$th bulb and perhaps some other bulbs, we compute the sharp lower bound on the number of bulbs that can be lit regardless of the action of the buttons. In the previous article we
Externí odkaz:
http://arxiv.org/abs/2410.02460
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications are found
Externí odkaz:
http://arxiv.org/abs/2406.02901
Publikováno v:
Math Scand 128 (2022) 147-160
Let $k$ be a natural number. We consider $k$-times continuously-differentiable real-valued functions $f:E\to\mathbb{R}$, where $E$ is some interval on the line having positive length. For $0<\alpha<1$ let $I_\alpha(f)$ denote the set of values $y\in\
Externí odkaz:
http://arxiv.org/abs/2010.11556
Autor:
O'Farrell, Anthony G.
We consider formal maps in any finite dimension $d$ with coefficients in an integral domain $K$ with identity. Those invertible under formal composition form a group $\mathcal{G}$. We consider the centraliser $C_g$ of an element $g\in\mathcal{G}$ whi
Externí odkaz:
http://arxiv.org/abs/2010.07177
Autor:
O'Farrell, Anthony G.
The classical Riordan groups associated to a given commutative ring are groups of infinite matrices (called Riordan arrays) associated to pairs of formal power series in one variable. The Fundamental Theorem of Riordan Arrays relates matrix multiplic
Externí odkaz:
http://arxiv.org/abs/2009.14130
Autor:
O'Farrell, Anthony G.
We consider the behaviour at a boundary point of an open subset $U\subset\mathbb{C}$ of distributions that are holomorphic on $U$ and belong to what are called negative Lipschitz classes. The result explains the significance for holomorphic functions
Externí odkaz:
http://arxiv.org/abs/1806.09979
Autor:
O'Farrell, Anthony G.
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions exhibit so
Externí odkaz:
http://arxiv.org/abs/1605.05196
Autor:
Nikou, Azadeh, O'Farrell, Anthony G.
This paper is about the connection between certain Banach-algebraic properties of a commutative Banach algebra $E$ with unit and the associated commutative Banach algebra $C(X,E)$ of all continuous functions from a compact Hausdorff space $X$ into $E
Externí odkaz:
http://arxiv.org/abs/1512.09303