Results 11 to 20 of about 1,385 (141)

New Inequalities and an Integral Expression for the 𝒜-Berezin Number

Journal of Mathematics
This work examines a reproducing kernel Hilbert space XF,·,· constructed on a nonempty set F. Our investigation focuses on the A-Berezin number and the A-Berezin norm, where A denotes a positive bounded linear operator acting on XF.
Salma Aljawi, Ahad Alotaibi, Cristian Conde, Kais Feki   +3 more
doaj   +2 more sources

Quantitative Mapping of Fibrotic Tissue Mechanics via Brillouin Spectroscopy. [PDF]

J Biophotonics
Brillouin spectroscopy distinguishes fibrotic from healthy tissue based on localized stiffness changes and enables real‐time monitoring of dynamic alterations in viscoelastic properties during fibrogenesis.ABSTRACTFibrosis is a pathological scarring process that disrupts tissue architecture, and is characterized by excessive extracellular matrix (ECM ...
Cheburkanov V, Jung S, Berezin MY, Yakovlev VV.   +3 more
europepmc   +2 more sources

REVERSE INEQUALITIES FOR THE BEREZIN NUMBER OF OPERATORS

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2022
For a bounded linear operator $A$ on a reproducing kernel Hilbert space $\mathcal{H}(Ω)$, with normalized reproducing kernel $\widehat{k}_λ = \frac{k_λ}{\lVert k_λ\lVert}$, the Berezin symbol, Berezin number and Berezin norm are defined respectively by $\widetilde{A}(λ) = \langle A\widehat{k}_λ,\widehat{k}_λ\rangle$, $ber(A) = \sup_{λ\inΩ}\left ...
Garayev, Mubariz, Guediri, Hocine, Altwaijry, Najla   +2 more
openaire   +2 more sources

A characterization of operators via Berezin symbol and related questions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
In this paper, we characterize the hyponormal operators with regard to Berezin symbol and reproducing kernel. Also, we demonstrate several Berezin number inequalities for bounded linear operators.
Yamancı Ulaş
doaj   +1 more source

A Generalized Norm on Reproducing Kernel Hilbert Spaces and Its Applications

Axioms, 2023
The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm of bounded linear ...
Najla Altwaijry, Kais Feki, Nicuşor Minculete   +2 more
doaj   +1 more source

More Correct Berezin Symbol Inequalities

Dera Natung Government College Research Journal, 2023
The purpose of this research is to show bounds for some Berezin number inequalities in an innovative approach. Some inequalities have been proven using the improvement of the Hermite-Hadamard inequality.
Hamdullah Başaran, Mehmet Gurdal
doaj   +1 more source

Artan Operatör Konveks Fonksiyon İçin Berezin Sayı Eşitsizliği

Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2021
Normalleştirilmiş $K_{\lambda}:=\frac{k_{\lambda}}{\left\Vert k_{\lambda}\right\Vert_{\mathcal{H}}}$, üretici çekirdekli $\mathcal{H}\left( \Omega\right) $, Hilbert uzayı üzerinde $A$ sınırlı lineer operatör için Berezin sembolü ve Berezin sayısı ...
Mehmet Gürdal, Hamdullah Başaran, Mualla Birgül Huban   +2 more
doaj   +1 more source

Complete refinements of the Berezin number inequalities [PDF]

Journal of Mathematical Inequalities, 2019
In this paper, several refinements of the Berezin number inequalities are obtained. We generalize inequalities involving powers of the Berezin number for product of two operators acting on a reproducing kernel Hilbert space $\mathcal H=\mathcal H(Ω)$ and also improve them.
Hajmohamadi, Monire, YAMANCI, Ulaş, Lashkaripour, Rahmatollah, Bakherad, Mojtaba   +3 more
openaire   +5 more sources

An extension of the Euclidean Berezin number

Filomat, 2023
The Berezin transform ? of an operator A, acting on the reproducing kernel Hilbert space H = H(?) over some (non-empty) set ?, is defined by ?(?) = ?A?k?,?k?? (? ? ?), where ?k? = k?/?k?? is the normalized reproducing kernel of H. The Berezin number of an operator A is defined by ber(A) = sup ??? ??(?)? = sup ??? ??A?k?,?k???.
Nooshin Eslami Mahdiabadi, Mojtaba Bakherad   +1 more
openaire   +1 more source

Numerical radius, Berezin number, and Berezin norm inequalities for sums of operators

Turkish Journal of Mathematics, 2023
The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space.
Altwaijry, Najla, Feki, Kais, Minculete, Nicusor   +2 more
openaire   +1 more source