77 citations · 956 across the 77 of their papers we have counts for
83 papers
Spectral minimal partitions of combinatorial graphs
Matthias Hofmann, James B. Kennedy, Delio Mugnolo +1
This paper investigates spectral minimal partitions for weighted graphs, thus extending the extensive class of results that are currently available on domains and, to a lesser exte…
The role of expanders in the spectral geometry of metric graphs
Delio Mugnolo
After reviewing combinatorial and spectral definitions of expanders, we use precise lower bounds on Ramanujan graphs to investigate upper bounds -- and, specifically, the lack ther…
Ornstein--Uhlenbeck semigroup on rooted trees
Sahiba Arora, Marjeta Kramar Fijavž, Delio Mugnolo +1
We study Ornstein--Uhlenbeck operators on rooted metric trees equipped with a Gaussian-type measure. Using form methods, we construct Dirichlet and Neumann realisations correspondi…
Semigroups For Initial-Boundary Value Problems
Marjeta Kramar, Delio Mugnolo, Rainer Nagel
We review the theory of one-sided coupled operator matrices with a focus on evolution equations with inhomogeneous boundary conditions. (The original article had no abstract.)
Theory And Applications Of One-Sided Coupled Operator Matrices
Marjeta Kramar, Delio Mugnolo, Rainer Nagel
The theory of one-sided coupled operator matrices, recently introduced by K.-J. Engel, is an abstract framework for concrete initial value problems and allows complete information…
A semigroup analogue of the Fonf--Lin--Wojtaszczyk ergodic characterization of reflexive Banach spaces with a basis
Delio Mugnolo
In analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space with a basis. (i) is finite-dimensional if…
Non-Markovian heat flows on directed hypergraphs
Delio Mugnolo
We introduce a semigroup framework for Laplacians on directed hypergraphs, extending the classical heat flow models on graphs and establishing hypergraphs as prototypical models fo…
On Spectral Properties of Restricted Fractional Laplacians with Self-adjoint Boundary Conditions on a Finite Interval
Jussi Behrndt, Markus Holzmann, Delio Mugnolo
We describe all self-adjoint realizations of the restricted fractional Laplacian with power on a bounded interval by imposing boundary conditions…
On the heat content of compact quantum graphs
Patrizio Bifulco, Delio Mugnolo
We study the heat content for Laplacians on compact, finite metric graphs with Dirichlet conditions imposed at the "boundary" (i.e., a given set of vertices). We prove a closed for…
Towards a theory of eigenvalue asymptotics on infinite metric graphs: the case of diagonal combs
James B. Kennedy, Delio Mugnolo, Matthias Täufer
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 poss…
On solitary waves for the Korteweg--de Vries equation on metric star graphs
Delio Mugnolo, Diego Noja, Christian Seifert
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…
Mean distance on metric graphs
Luís N. Baptista, James B. Kennedy, Delio Mugnolo
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 ex…
On the -torsional rigidity of combinatorial graphs
Patrizio Bifulco, Delio Mugnolo
We study the -\emph{torsion function} and the corresponding -\emph{torsional rigidity} associated with -Laplacians and, more generally, -Schrödinger operators, for $1<p…
On the Lipschitz continuity of the heat kernel
Patrizio Bifulco, Delio Mugnolo
We study integral kernels of strongly continuous semigroups on Lebesgue spaces over metric measure spaces. Based on semigroup smoothing properties and abstract Morrey-type inequali…
Sturm-Liouville Problems And Global Bounds By Small Control Sets And applications to quantum graphs
Michela Egidi, Delio Mugnolo, Albrecht Seelmann
We develop a Logvinenko--Sereda theory for one-dimensional vector-valued self-adjoint operators. We thus deliver upper bounds on -norms of eigenfunctions -- and linear combina…
Pointwise eigenvector estimates by landscape functions: some variations on the Filoche--Mayboroda--van den Berg bound
Delio Mugnolo
Landscape functions are a popular tool used to provide upper bounds for eigenvectors of Schrödinger operators on domains. We review some known results obtained in the last ten year…
Distinguishing co-spectral quantum graphs by scattering
Delio Mugnolo, Vyacheslav Pivovarchik
We propose a simple method for resolution of co-spectrality of Schrödinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the -funct…
On The Spectrum Of Infinite Quantum Graphs
Marco Düfel, James B. Kennedy, Delio Mugnolo +2
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…
Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap
Gregory Berkolaiko, James B. Kennedy, Pavel Kurasov +1
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 torsional rigidity and ground-state energy of compact quantum graphs
Delio Mugnolo, Marvin Plümer
We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least o…
Ornstein--Uhlenbeck Semigroups on Star Graphs
Delio Mugnolo, Abdelaziz Rhandi
We prove first existence of a classical solution to a class of parabolic problems with unbounded coefficients on metric star graphs subject to Kirchhoff-type conditions. The result…
The wave equation with acoustic boundary conditions on non-locally reacting surfaces
Delio Mugnolo, Enzo Vitillaro
The aim of the paper is to study the problem in , on , $v_t =\partial_…
Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph
Matthias Erbar, Dominik Forkert, Jan Maas +1
This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou-Brenier formula for the Wasserstein distance, which establishe…
Hubs-biased resistance distances on graphs and networks
Ernesto Estrada, Delio Mugnolo
We define and study two new kinds of "effective resistances" based on hubs-biased -- hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these…