Weighted Paley-Wiener theorem, with applications to stability of the linear multi-step methods for Volterra equations in Hilbert spaces

DOI10.1016/j.jmaa.2011.12.035zbMath1243.65164OpenAlexW2026722381MaRDI QIDQ764944

Da Xu

Publication date: 16 March 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.12.035

zbMATH Keywords

stabilityintegro-differential equationslinear multi-step time discretizationlinear Volterra-type equationPaley-Wiener Theorem

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Volterra integral equations (45D05) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (4)

Second-order difference approximations for Volterra equations with the completely monotonic kernels ⋮ Numerical solution of evolutionary integral equations with completely monotonic kernel by Runge–Kutta convolution quadrature ⋮ The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence ⋮ Decay properties for the numerical solutions of a partial differential equation with memory

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic behaviour of resolvents of abstract Volterra equations
• Stability of the difference type methods for linear Volterra equations in Hilbert spaces
• Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations
• Positivity and regularity of hyperbolic Volterra equations in Banach spaces
• Convolution quadrature and discretized operational calculus. I
• Convolution quadrature and discretized operational calculus. II
• Viscoelastic and boundary feedback damping: Precise energy decay rates when creep modes are dominant
• On convolution quadrature and Hille-Phillips operational calculus
• On the quadrature error in operational quadrature methods for convolutions
• Stability of Volterra equations with measure kernels in Banach spaces
• Convolution quadrature revisited
• A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces
• On Volterra integral equations with nonnegative integrable resolvents
• Nonlinear Volterra integrodifferential systems with L\(^1\)-kernels
• Discretized Fractional Calculus
• Uniform l1 behaviour in a second-order difference-type method for a linear Volterra equation with completely monotonic kernel I: stability
• Convolution quadrature time discretization of fractional diffusion-wave equations
• Uniform Error Estimates of Operational Quadrature Methods for Nonlinear Convolution Equations on the Half-Line
• A Numerical Method for a Partial Integro-Differential Equation
• Structure of Resolvents of Volterra Integral and Integro-Differential Systems
• Local Analyticity in Weighted L 1 -Spaces and Applications to Stability Problems for Volterra Equations
• Variants of the Wiener-Levy Theorem, with Applications to Stability Problems for Some Volterra Integral Equations
• Abstract Linear and Nonlinear Volterra Equations Preserving Positivity
• Evolutionary Integral Equations and Applications
• A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties
• Notes on the Theory and Application of Fourier Transforms, III, IV, V, VI, VII
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• Operational Quadrature Methods for Wiener-Hopf Integral Equations
• A special stability problem for linear multistep methods

This page was built for publication: Weighted Paley-Wiener theorem, with applications to stability of the linear multi-step methods for Volterra equations in Hilbert spaces