Zobrazeno 1 - 10
of 76
pro vyhledávání: '"O'Loughlin, Ryan"'
The circuits comprising superconducting optoelectronic synapses, dendrites, and neurons are described by numerically cumbersome and formally opaque coupled differential equations. Reference 1 showed that a phenomenological model of superconducting lo
Externí odkaz:
http://arxiv.org/abs/2409.18016
The Crouzeix ratio $\psi(A)$ of an $N\times N$ complex matrix $A$ is the supremum of $\|p(A)\|$ taken over all polynomials $p$ such that $|p|\le 1$ on the numerical range of $A$. It is known that $\psi(A)\le 1+\sqrt{2}$, and it is conjectured that $\
Externí odkaz:
http://arxiv.org/abs/2409.14127
Given a compact convex planar domain $\Omega$ with non-empty interior, the classical Neumann's configuration constant $c_{\mathbb{R}}(\Omega)$ is the norm of the Neumann-Poincar\'e operator $K_\Omega$ acting on the space of continuous real-valued fun
Externí odkaz:
http://arxiv.org/abs/2407.19049
Autor:
Miheisi, Nazar, O'Loughlin, Ryan
We discuss generalizations of the Szeg\H{o} Limit Theorem to truncated Toeplitz operators. In particular, we consider compressions of Toeplitz operators to an increasing sequence of finite dimensional model spaces. We present two theorems. The first
Externí odkaz:
http://arxiv.org/abs/2404.03087
We study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator theorists. We pose many open questions that should interest the field.
Externí odkaz:
http://arxiv.org/abs/2306.14807
Autor:
O'Loughlin, Ryan, Virtanen, Jani
For a matrix $A$ which satisfies Crouzeix's conjecture, we construct several classes of matrices from $A$ for which the conjecture will also hold. We discover a new link between cyclicity and Crouzeix's conjecture, which shows that Crouzeix's Conject
Externí odkaz:
http://arxiv.org/abs/2306.12183
Autor:
O'Loughlin, Ryan
In this paper, we study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particular, we determine necessary and sufficient conditions for when a 3-by-3
Externí odkaz:
http://arxiv.org/abs/2202.01745
Autor:
O'Loughlin, Ryan, Virtanen, Jani
Publikováno v:
In Linear Algebra and Its Applications 15 September 2024 697:277-292
Autor:
O'Loughlin, Ryan
This paper characterises the dual of the model space $K_I^1$, where $I$ is an inner function, intersected with the shifted Hardy space, $z H^1$. With this duality result, it is then shown that every bounded truncated Toeplitz operator on the model sp
Externí odkaz:
http://arxiv.org/abs/2107.09115
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with $4 \times 4$ matrix symbols. We discuss their norm, their kernel, Fredhomlness, invertibility and
Externí odkaz:
http://arxiv.org/abs/2012.14725