Harmonic functions and gravity localization
A bstract In models with extra dimensions, matter particles can be easily localized to a 'brane
world', but gravitational attraction tends to spread out in the extra dimensions unless they are …
world', but gravitational attraction tends to spread out in the extra dimensions unless they are …
Approximation, regularity and positivity preservation on Riemannian manifolds
S Pigola, D Valtorta, G Veronelli - Nonlinear Analysis, 2024 - Elsevier
The paper focuses on the L p-Positivity Preservation property (L p-PP for short) on a
Riemannian manifold (M, g). It states that any L p function u with 1< p<+∞, which solves …
Riemannian manifold (M, g). It states that any L p function u with 1< p<+∞, which solves …
positivity preservation and self-adjointness in incomplete Riemannian manifolds
A Bisterzo, G Veronelli - arXiv preprint arXiv:2310.11118, 2023 - arxiv.org
The aim of this paper is to prove a qualitative property, namely the preservation of positivity,
for Schr\" odinger-type operators acting on $ L^ p $ functions defined on (possibly …
for Schr\" odinger-type operators acting on $ L^ p $ functions defined on (possibly …
A tensor product approach to non-local differential complexes
M Hinz, J Kommer - Mathematische Annalen, 2024 - Springer
We study differential complexes of Kolmogorov–Alexander–Spanier type on metric measure
spaces associated with unbounded non-local operators, such as operators of fractional …
spaces associated with unbounded non-local operators, such as operators of fractional …
Differential complexes for local Dirichlet spaces, and non-local-to-local approximations
M Hinz, J Kommer - arXiv preprint arXiv:2407.07252, 2024 - arxiv.org
We study differential $ p $-forms on non-smooth and possibly fractal metric measure spaces,
endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the …
endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the …
Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity
A Inoue, S Ku, J Masamune… - arXiv preprint arXiv …, 2024 - arxiv.org
We give two characterizations for the essential self-adjointness of the weighted Laplacian on
birth-death chains. The first involves the edge weights and vertex measure and is classically …
birth-death chains. The first involves the edge weights and vertex measure and is classically …
Lp positivity preservation and self-adjointness of Schrödinger operators on incomplete Riemannian manifolds
A Bisterzo, G Veronelli - Proceedings of the Royal Society of …, 2024 - cambridge.org
Lp positivity preservation and self-adjointness of Schrödinger operators on incomplete
Riemannian manifolds Page 1 Proceedings of the Royal Society of Edinburgh, page 1 of 19 …
Riemannian manifolds Page 1 Proceedings of the Royal Society of Edinburgh, page 1 of 19 …
Capacities, Removable Sets and Lp-Uniqueness on Wiener Spaces
M Hinz, S Kang - Potential Analysis, 2021 - Springer
We prove the equivalence of two different types of capacities in abstract Wiener spaces. This
yields a criterion for the L p-uniqueness of the Ornstein-Uhlenbeck operator and its integer …
yields a criterion for the L p-uniqueness of the Ornstein-Uhlenbeck operator and its integer …