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Cosine families and semigroups really differ [PDF]

Journal of Evolution Equations, 2013
Let \(X\) be a Banach space and \(\mathcal{L}(X)\) the space of all bounded linear operators on \(X\). This paper investigates the differences between the theories of two \(\mathcal{L}(X)\)-valued functions: the cosine familes and the semigroups of linear operators on \(X\).
Wojciech Chojnacki, Adam Bobrowski
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On cosine families

Rendiconti Del Circolo Matematico Di Palermo, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khalil Moussa Ouja, Abdelkhalek El Amrani   +1 more
exaly   +2 more sources

Generalized Cosine Family

Journal of Elliptic and Parabolic Equations, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdelmjid Benmerrous, Lalla saadia Chadli, Abdelaziz Moujahid, M’hamed Elomari, Said Melliani   +4 more
openaire   +2 more sources

On Multivalued Cosine Families [PDF]

Journal of Applied Analysis, 2007
The author gives the following result: Let \(X\) be a real Banach space and let \(K\) be a closed convex cone in \(X\) such that \(\text{int\,}K\neq\emptyset\). Assume that \(\{F_t: t\in\mathbb{R}\}\) is a regular cosine family of continuous linear multifunctions \(F_t: K\to cc(X)\) and \(x\in F_t(x)\) for all \(x\in K\) and \(t\in\mathbb{R}\).
exaly   +2 more sources

LOCAL C-COSINE FAMILIES AND N-TIMES INTEGRATED LOCAL COSINE FAMILIES

Taiwanese Journal of Mathematics, 2004
For the investigation of ill-posed first-order abstract Cauchy problems, the theory of \(C\)-semigroups and \(n\)-times integrated semigroups has been developed and intensively studied in the last 20 years. The main technical tool in these investigations was the exhausting use of vector-valued Laplace transforms theory.
Takenaka, T., Piskarev, S.
exaly   +3 more sources

Demicompactness Properties for Uniformly Continuous Cosine Families

Mediterranean Journal of Mathematics, 2022
Let \(X\) be a Banach space and let \((C(t))_{t\in\mathbb{R}}\) be a strongly continuous cosine family with generator \(A\). Let \(S(t)\) be a related sine family. Denote \(\Psi_1=\{t>0: C(t)\text{ is demicompact}\}\) and \(\Psi_2=\{t>0: I-(tI-S(t))\text{ is demicompact}\}\). Let \(B\) be a compact operator in \(X\). By \(\tilde{C}\) and \(\tilde{S}\),
Asrar Elleuch, Aref Jeribi, Hedi Benkhaled   +2 more
exaly   +3 more sources

On bi-continuous cosine families

Quaestiones Mathematicae
In this article, we introduce and investigate bi-continuous cosine families. Those are inspired by the theory of bi-continuous semigroups which had an impact in the area of evolution equations in the last decades. The idea here is again that we equip the underlying Banach space with an additional locally convex topology.
Christian Budde
exaly   +3 more sources

Cosine families of operators and applications

Lecture Notes in Mathematics, 1986
Michiaki Watanabe
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