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Zero-two law for cosine families [PDF]

Journal of Evolution Equations, 2015
For $\left(C(t)\right)_{t \geq 0}$ being a strongly continuous cosine family on a Banach space, we show that the estimate $\limsup_{t\to 0^{+}}\|C(t) - I\| <2$ implies that $C(t)$ converges to $I$ in the operator norm. This implication has become known as the zero-two law.
Felix L. Schwenninger, Hans J. Zwart
exaly   +4 more sources

On close-to-scalar one-parameter cosine families

Journal of Mathematical Analysis and Applications, 2015
Let \(\mathbf{A}\) be a complex Banach algebra with unit e. Let \(a\in\mathbf{A}\) be invertible and \(\sup_{n\in\mathbb{Z}}\|a^n\|
Wojciech Chojnacki, Adam Bobrowski, Adam Gregosiewicz   +2 more
exaly   +4 more sources

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The Dimension Paradox in Parameter Space of Cosine Family

Chinese Annals of Mathematics, Series B, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Xiaojie, Qiu, Weiyuan
openaire   +1 more source

On the regular cosine family of linear correspondences

Aequationes Mathematicae, 2012
Let \(X\) and \(Y\) be normed spaces, \(X_0\) the completion of \(X\), \(C \subset X\) a convex cone with nonempty interior. For a continuous linear correspondence (multivalued linear operator) \(\varphi : C \multimap Y,\) the authors prove the existence of a unique continuous linear extension on \(cl_{X_0}C\).
Kourosh Nourouzi, Masoumeh Aghajani
exaly   +2 more sources

Cosine Families of Unbounded Operators

Applicable Analysis, 1985
The initial value problem for is shown to have a unique strong solution provided the spectrum of the linear time-independent operator –A exhibits a parabolic condensation along the negative real axis. The particular case when A is a nonsymmetric perturbation of a self-adjoint elliptic partial differential operator does not fit in the commonly known ...
R. P. Gilbert, Hans Grabmüller, M. Sova
openaire   +1 more source

Commutativity of set-valued cosine families

Open Mathematics, 2014
AbstractLet K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If {F t: t ≥ 0} is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then $F_t \circ F_s (x) = F_s \circ F_t (x)fors,t
Smajdor Andrzej, Smajdor Wilhelmina
exaly   +4 more sources

A ZERO- LAW FOR COSINE FAMILIES

Journal of the Australian Mathematical Society, 2017
Let$a\in \mathbb{R}$, and let$k(a)$be the largest constant such that$\sup |\text{cos}(na)-\cos (nb)|<k(a)$for$b\in \mathbb{R}$implies that$b\in \pm a+2\unicode[STIX]{x1D70B}\mathbb{Z}$. We show that if a cosine sequence$(C(n))_{n\in \mathbb{Z}}$with values in a Banach algebra$A$satisfies$\sup _{n\geq 1}\Vert C(n)-\cos (na).1_{A}\Vert <k(a)$, then$
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Around Schwenninger and Zwart’s zero-two law for cosine families

Archiv Der Mathematik, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wojciech Chojnacki
exaly   +4 more sources

A family of cosine-sum windows for high-resolution measurements

2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), 2002
Special windows are used in spectral analysis to reduce the effect of spectral leakage. Windows with low sidelobe amplitude are necessary for the detection of small signals when highly dynamic spectra are concerned. The design of a family of cosine-sum windows with minimum sidelobes is described.
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On core entropy for cosine family

Sur l'entropie du cœur pour la famille cosinus L'entropie topologique est connue pour être une mesure de la complexité d'un système dynamique donné par l'itération d'une fonction continue. Pour les fonctions complexes dans tous les cas étudiés, elle s'avère constante, donc dans la dynamique complexe un autre concept est pris en compte ...
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