An ergodic approach to Laplace transforms on time scales
type: Item
instance of: scholarly article
title: An ergodic approach to Laplace transforms on time scales
zbMATH Open document ID: 1467.26020
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-06-14T00:00:00Z
review text: The authors examine the region of convergence for the Laplace transform on time scales (i.e., closed subsets of the real axis). They employ an (what they call) ergodic approach in order to both calculate (1) the region of convergence and (2) the inversion of the transform. It turns out that the problem (1) is closedly related to the problem of determining regions of stability for the time scale exponential function \(e_z(t,t_0)\). Concerning the problem (2) the authors use ergodic techniques to arrive at a solution, and so in the current paper they expound upon these notions and show how they can be used to think about the Laplace transform in an effective and efficient manner. \par The paper is carefully written and nicely illustrated using various related examples. In particular, its introduction contains an overview of the current state of the time scales theory.
Mathematics Subject Classification ID: 26E70
Mathematics Subject Classification ID: 37A25
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 7358707
zbMATH Keywords: Laplace transform
zbMATH Keywords: ergodic theory
zbMATH Keywords: time scale
author: Billy J. Jackson
author: John M. Davis
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125231
OpenAlex ID: W3156316888
cites work: Q5852536
cites work: Q4914674
cites work: Isoperimetric problems on time scales with nabla derivatives
cites work: Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales
cites work: Rational Solutions for the Time-Fractional Diffusion Equation
cites work: A Kernel Compression Scheme for Fractional Differential Equations
cites work: Q5446749
cites work: Stability and stabilizability of linear time-delay systems on homogeneous time scales
cites work: The convolution on time scales
cites work: Properties of the Laplace transform on time scales with arbitrary graininess
cites work: Further properties of the Laplace transform on time scales with arbitrary graininess
cites work: Inequalities on time scales: a survey
cites work: Global stability of complex-valued neural networks on time scales
cites work: The Kalman filter for linear systems on time scales
cites work: Optimal sampled-data control, and generalizations on time scales
cites work: On different types of stability for linear delay dynamic equations
cites work: Asymptotic and Transient Mean-Square Properties of Stochastic Systems Arising in Ecology, Fluid Dynamics, and System Control
cites work: Exponential stabilization of well-posed systems by colocated feedback
cites work: Stability for time varying linear dynamic systems on time scales
cites work: A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems
cites work: Controllability, Observability, Realizability, and Stability of Dynamic Linear Systems
cites work: The Laplace transform on time scales revisited
cites work: Bilateral Laplace transforms on time scales: convergence, convolution, and the characterization of stationary stochastic time series
cites work: Q5409616
cites work: Singular value conditions for stability of dynamic switched systems
cites work: Q4462032
cites work: A unified approach to high-gain adaptive controllers
cites work: Machine Learning of Space-Fractional Differential Equations
cites work: Diet Selection as a Differential Foraging Game
cites work: Lyapunov functions for time-scale dynamics on Riemannian geometries of the simplex
cites work: Q3995705
cites work: Analysis on measure chains - a unified approach to continuous and discrete calculus
cites work: Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems
cites work: An ergodic approach to Pötzsche-Siegmund-Wirth's region of exponential stability
cites work: Linear state feedback stabilisation on time scales
cites work: Q4963568
cites work: Applications of Laplace--Carleson Embeddings to Admissibility and Controllability
cites work: Hyperbolicity and solvability for linear systems on time scales
cites work: Stability by linear approximation for time scale dynamical systems
cites work: Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations. V. Small Shifts with Layer Behavior
cites work: On the analytical and numerical properties of the truncated Laplace transform. II
cites work: Laplace Transform Method for Parabolic Problems with Time-Dependent Coefficients
cites work: A Parallel Method for Backward Parabolic Problems Based on the Laplace Transformation
cites work: A Discretization of Caputo Derivatives with Application to Time Fractional SDEs and Gradient Flows
cites work: Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives
cites work: On the exponential stability of Samuelson model on some classes of times scales
cites work: A Spectral Order Method for Inverting Sectorial Laplace Transforms
cites work: Direct problems for poroelastic waves with fractional derivatives
cites work: Calculating Laplace Transforms in Terms of the Toda Molecule
cites work: On Stability and Stabilization of Perturbed Time Scale Systems with Gronwall Inequalities
cites work: Exponentials and Laplace transforms on nonuniform time scales
cites work: Nonlinear dynamic systems and optimal control problems on time scales
cites work: Mean square stability for systems on stochastically generated discrete time scales
cites work: The Kalman filter on stochastic time scales
cites work: A spectral characterization of exponential stability for linear time-invariant systems on time scales
cites work: The \((q,h)\)-Laplace transform on discrete time scales
cites work: A new definition of conformable fractional derivative on arbitrary time scales
cites work: On Passivity of Fractional Order Systems
cites work: Robust Permanence for Ecological Maps
cites work: Fast and Oblivious Convolution Quadrature

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An ergodic approach to Laplace transforms on time scales (DOI)
DOI: 10.1016/J.JMAA.2021.125231