Article
Mathematics, Applied
Isaac Z. Pesenson, Meyer Z. Pesenson
Summary: This paper introduces and proves Poincare-type inequalities to establish a sampling theory for signals on undirected weighted finite or infinite graphs, and develops an interpolation theory especially suited for community graphs with multiple clusters.
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Chao Huang, Qian Zhang, Jianfeng Huang, Lihua Yang
Summary: This paper studies the approximation of functions defined on combinatorial graphs in Paley-Wiener spaces and establishes inequalities for functions on graphs. Through the estimation of the decay of graph Fourier coefficients, it leads to a theory of approximation of functions on combinatorial graphs with potential applications in various fields.
JOURNAL OF APPROXIMATION THEORY
(2021)
Article
Mathematics, Applied
Minggang Fei, Yu Hu
Summary: In this paper, we prove various real Paley-Wiener theorems for the Fourier-Bessel transform associated with the Laplace-Bessel operator. These theorems have many applications in pure and applied mathematics. We characterize functions in the Lebesgue space L-?(p) (R-n), 1 ≤ p ≤ 8, by their Fourier-Bessel transforms vanishing outside polynomial domains and in a neighborhood of the origin. Finally, we present a stronger version of the real Paley-Wiener theorem for the Fourier-Bessel transform in L-?(p) (R-n).
COMPLEX ANALYSIS AND OPERATOR THEORY
(2023)
Article
Mathematics
Alberto Arenas, Oscar Ciaurri, Edgar Labarga
Summary: This paper continues the research on harmonic analysis associated with Jacobi expansions conducted in Arenas et al. (2020) and Arenas et al. (2022). It defines the corresponding Littlewood-Paley-Stein g(& alpha;,& beta;) and proves an equivalence of norms with weights for them, leading to a result for Laplace type multipliers.
JOURNAL OF APPROXIMATION THEORY
(2023)
Article
Mathematics, Applied
Hussain Al-Hammali, Adel Faridani
Summary: In this paper, a generalisation of the classical Shannon sampling theorem is presented, allowing for sampling sets that are perturbations of the set of zeros of a sine-type function, which may be non-equidistant and non-periodic.
APPLICABLE ANALYSIS
(2021)
Article
Mathematics
Anders Bjorn, Jana Bjorn, Juha Lehrback
Summary: In a complete metric space equipped with a doubling measure supporting a p-Poincare inequality, sharp growth and integrability results are proven for p-harmonic Green functions and their minimal p-weak upper gradients. These properties are determined by the growth of the measure near the singularity. Similar results are obtained for more general p-harmonic functions with poles and singular solutions of elliptic differential equations. The proofs rely on a new capacity estimate for annuli, which also characterizes zero capacity singletons and the p-parabolicity of the space.
JOURNAL D ANALYSE MATHEMATIQUE
(2023)
Article
Mathematics, Applied
Sadia Khalid, Josip Pecaric
Summary: This paper presents interesting identities and inequalities for real valued functions and r-convex functions, as well as generalizations of some Hardy-Littlewood-Polya type inequalities. The Cebygev functional and Gruss type inequalities are used to find bounds for remainders in the obtained identities. An intriguing result related to the Ostrowski type inequalities is also discussed.
Article
Statistics & Probability
Paul-Marie Samson
Summary: The Lott-Sturm-Villani theory of curvature on geodesic spaces has been extended to discrete graph spaces by C. Leonard, who replaced W-2-Wasserstein geodesics with Schrodinger bridges in the definition of entropic curvature. This paper analyses this property on discrete graphs and provides lower bounds for entropic curvature, as well as new Prekopa-Leindler type inequalities and transport-entropy inequalities related to concentration properties.
PROBABILITY THEORY AND RELATED FIELDS
(2022)
Article
Mathematics
Fernando Lopez-Garcia, Ignacio Ojea
Summary: This paper studies certain inequalities and a related result for weighted Sobolev spaces on Holder-alpha domains, where the weights are powers of the distance to the boundary. Results regarding the solvability of the divergence equation, as well as improved Poincare, fractional Poincare, and Korn inequalities, are obtained. The novelty of the approach lies in the use of a weighted discrete Hardy inequality and a sufficient condition that allows for the study of the weights of interest. The assumptions on the weight exponents in the results are weaker than those in the literature.
POTENTIAL ANALYSIS
(2023)
Article
Mathematics
Chris Guiver, Mark R. Opmeer
Summary: This paper considers the representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces using the Laplace transform as operator-valued multiplication operators. Characterizations of when such operators map continuously between certain interpolation spaces and/or Bessel potential spaces are provided, including boundedness and integrability properties of the symbol, also known as the transfer function in this setting. The Hilbert space case is considered and illustrated with examples.
INTEGRAL EQUATIONS AND OPERATOR THEORY
(2023)
Article
Automation & Control Systems
Wei Chen, Zidong Wang, Derui Ding, Gheorghita Ghinea, Hongjian Liu
Summary: This article investigates the distributed formation-containment (FC) control problem for a class of discrete-time multiagent systems (DT-MASs) under the event-triggered communication mechanism. A novel dynamic event-triggered (DET) mechanism is developed to save communication cost and improve resource utilization. Based on available relative outputs, a distributed FC control scheme under the DET mechanism is proposed for all leaders and followers. The goal is to design an FC controller such that all leaders achieve formation shape and all followers converge into a convex hull. The considered DT-MASs are decoupled into a diagonal form using the Laplacian matrix property and inequality technique, and two sufficient conditions are established to ensure the desired FC performance. The FC controller parameters are obtained based on the solutions to two matrix inequalities depending on the maximum and minimum nonzero eigenvalues of the Laplacian matrix. An illustrative example is provided to verify the effectiveness of the developed control scheme.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Mathematics
A. I. Bondal, I. Yu. Zhdanovskiy
Summary: This paper surveys contemporary results and applications of the theory of homotopes, introduces the notion of a well-tempered element of an associative algebra, and studies homotopes constructed from generalized Laplace operators.
RUSSIAN MATHEMATICAL SURVEYS
(2021)
