Zobrazeno 1 - 10
of 551
pro vyhledávání: '"Mugnolo, A"'
We examine diagonal combs, a recently identified class of infinite metric graphs whose properties depend on one parameter. These graphs exhibit a fascinating regime where they possess infinite volume while maintaining purely discrete spectrum for the
Externí odkaz:
http://arxiv.org/abs/2403.10708
We study the Korteweg--de Vries equation on a metric star graph and investigate existence of solitary waves on the metric graph in terms of the coefficients of the equation on each edge, the coupling condition at the central vertex of the star and th
Externí odkaz:
http://arxiv.org/abs/2402.08368
Autor:
Bifulco, Patrizio, Mugnolo, Delio
We study the $p$-\emph{torsion function} and the corresponding $p$-\emph{torsional rigidity} associated with $p$-Laplacians and, more generally, $p$-Schr\"odinger operators, for $1
Externí odkaz:
http://arxiv.org/abs/2312.14131
We introduce a natural notion of mean (or average) distance in the context of compact metric graphs, and study its relation to geometric properties of the graph. We show that it exhibits a striking number of parallels to the reciprocal of the spectra
Externí odkaz:
http://arxiv.org/abs/2312.04952
Autor:
Bifulco, Patrizio, Mugnolo, Delio
We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequalities, we give sufficient conditions for H\"older or Lipschitz continui
Externí odkaz:
http://arxiv.org/abs/2307.08889
Publikováno v:
J. Math. Anal. Appl. 535 (2024) 128101
We develop a Logvinenko--Sereda theory for one-dimensional vector-valued self-adjoint operators. We thus deliver upper bounds on $L^2$-norms of eigenfunctions -- and linear combinations thereof -- in terms of their $L^2$- and $W^{1,2}$-norms on small
Externí odkaz:
http://arxiv.org/abs/2304.10441
Autor:
Mugnolo, Delio
Landscape functions are a popular tool used to provide upper bounds for eigenvectors of Schr\"odinger operators on domains. We review some known results obtained in the last ten years, unify several approaches used to achieve such bounds, and extend
Externí odkaz:
http://arxiv.org/abs/2301.06126
We propose a simple method for resolution of co-spectrality of Schr\"odinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the $S$-functions of the corresponding scattering problems on these (non-compact)
Externí odkaz:
http://arxiv.org/abs/2211.05465
We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called Friedrichs and Neumann extensions. We introduce a new criterion for co
Externí odkaz:
http://arxiv.org/abs/2207.04024
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total length of t
Externí odkaz:
http://arxiv.org/abs/2206.10046