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Abstracts of the 16th Annual Meeting of the Israel Society for Neuroscience, November 25-27, 2007, Eilat, Israel. [PDF]
Neural Plast, 2007 europepmc +1 more source
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Some new relations between the Berezin number and the Berezin norm of operators
Rocky Mountain Journal of Mathematics, 2022For a bounded linear operator \(A\) on a reproducing kernel Hilbert space with reproducing kernel \(K(z,w)\), the Berezin symbol, Berezin norm and Berezin number of \(A\) are defined, respectively, by \[ \tilde A(w):=\langle Ak_w,k_w\rangle, \quad \|A\|_{Ber} := \sup_w \|Ak_w\|, \quad \operatorname{ber}(A) :=\sup_w |\tilde A(w)|, \] where \(k_w(z):=K(z,
Ramiz Tapdıgoğlu
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Refinements of some inequalities involving Berezin norms and Berezin number and related questions
Annali Dell'Universita Di Ferrara, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mubariz Garayev, Messaoud Guesba
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Numerical Functional Analysis and Optimization, 2023
In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain
Mehmet Gürdal, Kallol Paul
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In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain
Mehmet Gürdal, Kallol Paul
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A New Family of Semi-Norms Between the Berezin Radius and the Berezin Norm
Acta Applicandae MathematicaezbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mojtaba Bakherad +2 more
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Further Berezin Number and Berezin Norm Inequalities for Sums and Products of Operators
Complex Analysis and Operator TheoryzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Messaoud Guesba, Kallol Paul
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The Berezin Number, Norm of a Hankel Operator and Related Topics
Operator Theory: Advances and Applications, 2015We give, in terms of the Berezin number, necessary and sufficient conditions providing unitarity of an invertible operator. Also we obtain in terms of the Berezin number a new inequality for the norm of the Hankel operator \(H_{\varphi}\) which is better than the classical inequality \(\|H_{\varphi}\|\leq\|\varphi\|_{\infty}\) The Berezin number is ...
Mubariz Garayev
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Norm of Berezin transformon L p space
Journal D'Analyse Mathematique, 2008Let \(D\) be the unit disc in \(\mathbb C\) equipped with the standard Lebesgue measure \(\mu\). For \(K_\alpha(z, \xi)= (\alpha +1)\frac{(1-| \xi| ^2)^\alpha}{^(1-z\overline{\xi})^{\alpha + 2}}\), the operator \(G_\alpha: L^p(D) \to L^p(D)\), \((G_\alpha f)(z):= \frac1\pi \int_D| K_\alpha(z, \xi)| f(\xi)\,d\mu(\xi)\) is introduced.
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Berezin Number and Norm Inequalities for Operators in Hilbert and Semi-Hilbert Spaces
Mathematics Online First Collections, 2023Cristian Conde +2 more
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