Josef Kreulich - Academia.edu (original) (raw)

Papers by Josef Kreulich

Semigroup forum, Mar 19, 2024

Wirtschaftsinformatik & Management, Jun 1, 2018

Complex Analysis and Operator Theory, Oct 1, 2022

Wirtschaftsinformatik & Management, Oct 21, 2021

arXiv (Cornell University), Feb 26, 2017

It is shown how the linear method of the Yosida-approximation of the derivative applies to solve ... more It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral solution will provide regularity results. Moreover, this method applies to derive uniform convergence on the halfline, and therefore general results on boundedness and various types of asymptotic almost periodicity.

Semigroup Forum, Dec 1, 1994

ABSTRACT

Differential and Integral Equations, 1996

ABSTRACT

arXiv (Cornell University), May 26, 2020

This study uses methods to identify compactifications of semigroups S ⊂ L(X) that reside in the s... more This study uses methods to identify compactifications of semigroups S ⊂ L(X) that reside in the space L(X). These methods generalize, in some sense, the deLeeuw-Glicksberg theory to a greater class of vectors. This provides an abstract approach to several notions of almost periodicity, mainly involving right semitopological semigroups [32] and adjoint theory. Moreover, the given setting is refined to the case of bounded C0−semigroups.

arXiv (Cornell University), Aug 14, 2018

In this study, we refine the compactification presented by Witz [31] for general semigroups to th... more In this study, we refine the compactification presented by Witz [31] for general semigroups to the case of bounded C0-semigroups, herein involving adjoint theory for this class of operators. This approach considerably reduces the operator space in which the compactification is performed. Additionally, this approach leads to a decomposition of X ⊙ and to an extension of ergodic results to dual semigroups.

arXiv (Cornell University), Feb 26, 2017

In the underlying study it is shown how the linear method of the Yosida-approximation of the deri... more In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in& A(t,u_t)u(t) +\omega u(t), \ t \in \mathbb{R} \end{eqnarray*} Furthermore, in the case of finite and infinite delay we give an answer about whether the solution is bounded, periodic, almost periodic, or some kind of almost automorphy.

Advances in Nonlinear Analysis, Dec 2, 2016

We present sufficient conditions on the existence of solutions, with various specific almost peri... more We present sufficient conditions on the existence of solutions, with various specific almost periodicity properties, in the context of nonlinear, generally multivalued, non-autonomous initial value differential equations, du dt (t) ∈ A(t)u(t), t ≥ 0, u(0) = u 0 , and their whole line analogues, du dt (t) ∈ A(t)u(t), t ∈ ℝ, with a family {A(t)} t∈ℝ of ω-dissipative operators A(t) ⊂ X × X in a general Banach space X. According to the classical DeLeeuw-Glicksberg theory, functions of various generalized almost periodic types uniquely decompose in a "dominating" and a "damping" part. The second main object of the study-in the above context-is to determine the corresponding "dominating" part [A(⋅)] a (t) of the operators A(t), and the corresponding "dominating" differential equation, du dt (t) ∈ [A(⋅)] a (t)u(t), t ∈ ℝ.

arXiv (Cornell University), Dec 10, 2013

We show how the approach of Yosida approximation of the derivative serves to obtain new results f... more We show how the approach of Yosida approximation of the derivative serves to obtain new results for evolution systems. Using this method we obtain multivalued time dependent perturbation results. Additionally, translation invariant subspaces Y of the bounded and uniformly continuous functions are considered, to obtain criteria for the existence of solutions u ∈ Y to the equation u ′ (t) ∈ A(t)u(t) + ωu(t) + f (t), t ∈ R, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u ′ (t) ∈ A(t)u(t) + ωu(t) + f (t), t > 0, u(0) = u0, in general Banach spaces, where A(t) denotes a possibly nonlinear time dependent dissipative operator. Particular examples for the space Y are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior. Further, an application to functional differential equations is given.

Complex Analysis and Operator Theory

arXiv: Functional Analysis, Aug 14, 2018

In this study, we refine the compactification presented by Witz [31] for general semigroups to th... more In this study, we refine the compactification presented by Witz [31] for general semigroups to the case of bounded C0-semigroups, herein involving adjoint theory for this class of operators. This approach considerably reduces the operator space in which the compactification is performed. Additionally, this approach leads to a decomposition of X ⊙ and to an extension of ergodic results to dual semigroups.

This study uses the ideas of <cit.> to provide the dual of L^1(μ,X) in the positive and σ- ... more This study uses the ideas of <cit.> to provide the dual of L^1(μ,X) in the positive and σ- finite cases. This results in elegant necessary and sufficient criteria for weak compactness in L^1(S,μ,X) in the σ-finite case, using the ideas of <cit.> and <cit.>. Finally, the result of <cit.> is extended to compute the sun-dual of L^1(,X) with respect to the canonical translation semigroup, dropping the approximation property from X^*,, which is applied to obtain almost periodicity for integrals of non-smooth functions. Moreover, for evolution semigroups, it is shown that weak compactness of the orbits implies strong stability.

Differential and Integral Equations, 1996

arXiv: Dynamical Systems, 2017

In the underlying study it is shown how the linear method of the Yosida-approximation of the deri... more In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in& A(t,u_t)u(t) +\omega u(t), \ t \in \mathbb{R} \end{eqnarray*} Furthermore, in the case of finite and infinite delay we give an answer about whether the solution is bounded, periodic, almost periodic, or some kind of almost automorphy.

arXiv: Functional Analysis, 2020

The given study uses the methods to identify compactifications of semigroups SsubsetL(X),S\subset L(X),SsubsetL(X), whi... more The given study uses the methods to identify compactifications of semigroups SsubsetL(X),S\subset L(X),SsubsetL(X), which reside in the space L(X).L(X).L(X). This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The approach provides an abstract approach to several notions of almost periodicity, which mainly involving right semitopological semigroups \cite{RuppertLNM}, and the adjoint theory. Moreover, the given setting is refined to the case of bounded C_0−C_0-C_0−semigroups.

Abstract. This study uses the ideas of [11] to provide the dual of L(μ,X) in the positive and σ− ... more Abstract. This study uses the ideas of [11] to provide the dual of L(μ,X) in the positive and σ− finite cases. This results in elegant necessary and sufficient criteria for weak compactness in L(S, μ,X) in the σ−finite case, using the ideas of [5] and [4]. Finally, the result of [10] is extended to compute the sun-dual of L(R, X) with respect to the canonical translation semigroup, dropping the approximation property from X∗,, which is applied to obtain almost periodicity for integrals of non-smooth functions. Moreover, for evolution semigroups, it is shown that weak compactness of the orbits implies strong stability.

In this study, we refine the compactification presented by Witz \cite{Witz} for general semigroup... more In this study, we refine the compactification presented by Witz \cite{Witz} for general semigroups to the case of bounded C_0C_0C_0-semigroups, involving adjoint theory for this class of operators. This approach considerably reduces the operator space in which the compactification is performed. Additionally, this approach leads to a decomposition of XsunX^{\sun}Xsun and to an extension of ergodic results to dual semigroups.

Semigroup forum, Mar 19, 2024

Wirtschaftsinformatik & Management, Jun 1, 2018

Complex Analysis and Operator Theory, Oct 1, 2022

Wirtschaftsinformatik & Management, Oct 21, 2021

arXiv (Cornell University), Feb 26, 2017

It is shown how the linear method of the Yosida-approximation of the derivative applies to solve ... more It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral solution will provide regularity results. Moreover, this method applies to derive uniform convergence on the halfline, and therefore general results on boundedness and various types of asymptotic almost periodicity.

Semigroup Forum, Dec 1, 1994

ABSTRACT

Differential and Integral Equations, 1996

ABSTRACT

arXiv (Cornell University), May 26, 2020

This study uses methods to identify compactifications of semigroups S ⊂ L(X) that reside in the s... more This study uses methods to identify compactifications of semigroups S ⊂ L(X) that reside in the space L(X). These methods generalize, in some sense, the deLeeuw-Glicksberg theory to a greater class of vectors. This provides an abstract approach to several notions of almost periodicity, mainly involving right semitopological semigroups [32] and adjoint theory. Moreover, the given setting is refined to the case of bounded C0−semigroups.

arXiv (Cornell University), Aug 14, 2018

In this study, we refine the compactification presented by Witz [31] for general semigroups to th... more In this study, we refine the compactification presented by Witz [31] for general semigroups to the case of bounded C0-semigroups, herein involving adjoint theory for this class of operators. This approach considerably reduces the operator space in which the compactification is performed. Additionally, this approach leads to a decomposition of X ⊙ and to an extension of ergodic results to dual semigroups.

arXiv (Cornell University), Feb 26, 2017

In the underlying study it is shown how the linear method of the Yosida-approximation of the deri... more In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in& A(t,u_t)u(t) +\omega u(t), \ t \in \mathbb{R} \end{eqnarray*} Furthermore, in the case of finite and infinite delay we give an answer about whether the solution is bounded, periodic, almost periodic, or some kind of almost automorphy.

Advances in Nonlinear Analysis, Dec 2, 2016

We present sufficient conditions on the existence of solutions, with various specific almost peri... more We present sufficient conditions on the existence of solutions, with various specific almost periodicity properties, in the context of nonlinear, generally multivalued, non-autonomous initial value differential equations, du dt (t) ∈ A(t)u(t), t ≥ 0, u(0) = u 0 , and their whole line analogues, du dt (t) ∈ A(t)u(t), t ∈ ℝ, with a family {A(t)} t∈ℝ of ω-dissipative operators A(t) ⊂ X × X in a general Banach space X. According to the classical DeLeeuw-Glicksberg theory, functions of various generalized almost periodic types uniquely decompose in a "dominating" and a "damping" part. The second main object of the study-in the above context-is to determine the corresponding "dominating" part [A(⋅)] a (t) of the operators A(t), and the corresponding "dominating" differential equation, du dt (t) ∈ [A(⋅)] a (t)u(t), t ∈ ℝ.

arXiv (Cornell University), Dec 10, 2013

We show how the approach of Yosida approximation of the derivative serves to obtain new results f... more We show how the approach of Yosida approximation of the derivative serves to obtain new results for evolution systems. Using this method we obtain multivalued time dependent perturbation results. Additionally, translation invariant subspaces Y of the bounded and uniformly continuous functions are considered, to obtain criteria for the existence of solutions u ∈ Y to the equation u ′ (t) ∈ A(t)u(t) + ωu(t) + f (t), t ∈ R, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u ′ (t) ∈ A(t)u(t) + ωu(t) + f (t), t > 0, u(0) = u0, in general Banach spaces, where A(t) denotes a possibly nonlinear time dependent dissipative operator. Particular examples for the space Y are spaces of functions with various almost periodicity properties and more general types of asymptotic behavior. Further, an application to functional differential equations is given.

Complex Analysis and Operator Theory

arXiv: Functional Analysis, Aug 14, 2018

In this study, we refine the compactification presented by Witz [31] for general semigroups to th... more In this study, we refine the compactification presented by Witz [31] for general semigroups to the case of bounded C0-semigroups, herein involving adjoint theory for this class of operators. This approach considerably reduces the operator space in which the compactification is performed. Additionally, this approach leads to a decomposition of X ⊙ and to an extension of ergodic results to dual semigroups.

This study uses the ideas of <cit.> to provide the dual of L^1(μ,X) in the positive and σ- ... more This study uses the ideas of <cit.> to provide the dual of L^1(μ,X) in the positive and σ- finite cases. This results in elegant necessary and sufficient criteria for weak compactness in L^1(S,μ,X) in the σ-finite case, using the ideas of <cit.> and <cit.>. Finally, the result of <cit.> is extended to compute the sun-dual of L^1(,X) with respect to the canonical translation semigroup, dropping the approximation property from X^*,, which is applied to obtain almost periodicity for integrals of non-smooth functions. Moreover, for evolution semigroups, it is shown that weak compactness of the orbits implies strong stability.

Differential and Integral Equations, 1996

arXiv: Dynamical Systems, 2017

In the underlying study it is shown how the linear method of the Yosida-approximation of the deri... more In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in& A(t,u_t)u(t) +\omega u(t), \ t \in \mathbb{R} \end{eqnarray*} Furthermore, in the case of finite and infinite delay we give an answer about whether the solution is bounded, periodic, almost periodic, or some kind of almost automorphy.

arXiv: Functional Analysis, 2020

The given study uses the methods to identify compactifications of semigroups SsubsetL(X),S\subset L(X),SsubsetL(X), whi... more The given study uses the methods to identify compactifications of semigroups SsubsetL(X),S\subset L(X),SsubsetL(X), which reside in the space L(X).L(X).L(X). This method generalizes in some sense the deLeeuw-Glicksberg-Theory to a greater class of functions. The approach provides an abstract approach to several notions of almost periodicity, which mainly involving right semitopological semigroups \cite{RuppertLNM}, and the adjoint theory. Moreover, the given setting is refined to the case of bounded C_0−C_0-C_0−semigroups.

Abstract. This study uses the ideas of [11] to provide the dual of L(μ,X) in the positive and σ− ... more Abstract. This study uses the ideas of [11] to provide the dual of L(μ,X) in the positive and σ− finite cases. This results in elegant necessary and sufficient criteria for weak compactness in L(S, μ,X) in the σ−finite case, using the ideas of [5] and [4]. Finally, the result of [10] is extended to compute the sun-dual of L(R, X) with respect to the canonical translation semigroup, dropping the approximation property from X∗,, which is applied to obtain almost periodicity for integrals of non-smooth functions. Moreover, for evolution semigroups, it is shown that weak compactness of the orbits implies strong stability.

In this study, we refine the compactification presented by Witz \cite{Witz} for general semigroup... more In this study, we refine the compactification presented by Witz \cite{Witz} for general semigroups to the case of bounded C_0C_0C_0-semigroups, involving adjoint theory for this class of operators. This approach considerably reduces the operator space in which the compactification is performed. Additionally, this approach leads to a decomposition of XsunX^{\sun}Xsun and to an extension of ergodic results to dual semigroups.