Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem
type: Item
instance of: scholarly article
title: Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem
author: Chao Wang
author: Guangzhou Qin
author: Ravi P. Agarwal
published in: Advances in Mathematics
publication date: 2022-11-23T00:00:00Z
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 7622192
zbMATH Keywords: quaternionic exponentially dichotomous operators
zbMATH Keywords: direct sum decomposition of quaternionic Banach space
zbMATH Keywords: slice quaternionic Banach algebra
zbMATH Keywords: perturbation invariance
zbMATH Keywords: Cauchy problems of quaternionic evolution equations
zbMATH Keywords: \(S\)-spectrum
MaRDI profile type: Publication
full work available at URL: j.aim.2022.108747
OpenAlex ID: W4306408640
cites work: Q3127106
cites work: Fixed point theory and applications
cites work: The spectral theorem for quaternionic unbounded normal operators based on the \(S\)-spectrum
cites work: Q4650838
cites work: Shorter Notes: Strongly Continuous Semigroups, Weak Solutions, and the Variation of Constants Formula
cites work: Smooth invariant manifolds in Banach spaces with nonuniform exponential dichotomy
cites work: A Grobman--Hartman theorem for nonuniformly hyperbolic dynamics
cites work: Robustness of discrete dynamics via Lyapunov sequences
cites work: Q5431024
cites work: Nonuniform spectrum on Banach spaces
cites work: Perturbation of normal quaternionic operators
cites work: Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces
cites work: Unbounded perturbation of the exponential dichotomy for evolution equations
cites work: Nonuniform dichotomy spectrum and reducibility for nonautonomous equations
cites work: Fractional powers of quaternionic operators and Kato’s formula using slice hyperholomorphicity
cites work: On some properties of the quaternionic functional calculus
cites work: On the formulations of the quaternionic functional calculus
cites work: The quaternionic evolution operator
cites work: A new functional calculus for noncommuting operators
cites work: Extension results for slice regular functions of a quaternionic variable
cites work: Slice monogenic functions
cites work: A Cauchy kernel for slice regular functions
cites work: Non-commutative functional calculus: unbounded operators
cites work: Duality theorems for slice hyperholomorphic functions
cites work: Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
cites work: Spectral theory on the S-spectrum for quaternionic operators
cites work: An introduction to hyperholomorphic spectral theories and fractional powers of vector operators
cites work: A new construction of homogeneous quaternionic manifolds and related geometric structures
cites work: On certain Kähler quotients of quaternionic Kähler manifolds
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic S-Functional Calculus and Spectral Operators
cites work: A new approach to Cullen-regular functions of a quaternionic variable
cites work: A new theory of regular functions of a quaternionic variable
cites work: Slice regular semigroups
cites work: Slice regular functions on real alternative algebras
cites work: Q4382291
cites work: Q3244654
cites work: The Weyl calculus and Clifford analysis
cites work: Q4946766
cites work: Linear Quaternion Differential Equations: Basic Theory and Fundamental Results
cites work: Commutativity of quaternion‐matrix–valued functions and quaternion matrix dynamic equations on time scales
cites work: Exponentially dichotomous operators and applications
cites work: Quaternion Zernike spherical polynomials
cites work: Constructing prolate spheroidal quaternion wave functions on the sphere
cites work: Real Quaternionic Calculus Handbook
cites work: Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space
cites work: Hilbert transforms on the sphere with the Clifford algebra setting
cites work: Topics in quaternion linear algebra
cites work: Existence of dichotomies and invariant splittings for linear differential systems. I
cites work: Existence of dichotomies and invariant splittings for linear differential systems. II
cites work: Existence of dichotomies and invariant splittings for linear differential systems. III
cites work: Dynamics of evolutionary equations
cites work: Dichotomy spectrum for nonautonomous differential equations
cites work: REDUCIBILITY OF NONAUTONOMOUS LINEAR DIFFERENTIAL EQUATIONS
cites work: On decompositions of the Clifford valued Hilbert space and their applications to boundary value problems
cites work: Q3966611
cites work: Theory of translation closedness for time scales. With applications in translation functions and dynamic equations
cites work: General theory of the higher-order quaternion linear difference equations via the complex adjoint matrix and the quaternion characteristic polynomial

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (cites work)
cites work: A new quaternion hyper-complex space with hyper argument and basic functions via quaternion dynamic equations

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (cites work)
cites work: Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (cites work)
cites work: Quaternionic-valued ordinary differential equations. The Riccati equation

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (cites work)
cites work: Global structure of quaternion polynomial differential equations

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (cites work)
cites work: Nonuniform dichotomy spectrum and normal forms for nonautonomous differential systems

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (cites work)
cites work: Admissibility and roughness of nonuniform exponential dichotomies for difference equations

Quaternionic exponentially dichotomous operators through \(S\)-spectral splitting and applications to Cauchy problem (DOI)
DOI: 10.1016/J.AIM.2022.108747