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Berezin number inequalities for operators [PDF]

Concrete Operators, 2019
The Berezin transform à of an operator A, acting on the reproducing kernel Hilbert space ℋ = ℋ (Ω) over some (non-empty) set Ω, is defined by Ã(λ) = 〉Aǩ λ, ǩ λ〈 (λ ∈ Ω), where k⌢λ=kλ‖kλ‖${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown ...
Mojtaba Bakherad
exaly   +4 more sources

On Berezin norm and Berezin number inequalities for sum of operators

Demonstratio Mathematica
The aim of this study is to obtain several inequalities involving the Berezin number and the Berezin norm for various combinations of operators acting on a reproducing kernel Hilbert space.
Najla Altwaijry, Nicusor Minculete, Kais Feki   +2 more
exaly   +4 more sources

Some New Estimates for the Berezin Number of Hilbert Space Operators

Axioms, 2022
In this paper, we have developed new estimates of some estimates involving the Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space HΩ.
Najla Altwaijry, Kais Feki, Nicuşor Minculete   +2 more
doaj   +2 more sources

A POLE P286R-Mutated Hepatoid Adenocarcinoma of the Lung Showing Substantial Response to Immune Checkpoint Inhibition. [PDF]

Cancer Rep (Hoboken)
ABSTRACT Background Hepatoid adenocarcinoma of the lung (HAL) is a rare form of lung cancer with histological and morphological properties of hepatocellular carcinoma, characterized by an aggressive course of the disease and unfavorable prognosis. Given the rarity of the pathology and the lack of unambiguous therapeutic protocols, descriptions of ...
Chernev A, Kaurtseva A, Abasov R, Enikeev R, Gegelia N, Abdrakova G, Usman N, Druy A, Raskin G.   +8 more
europepmc   +2 more sources

Berezin Yarıçapı İçin Diğer Eşitsizlikler [PDF]

Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2023
İşlevsel Hilbert uzayları, istatistik, yaklaşım teorisi, grup temsili teorisi, vb. dahil olmak üzere birçok alanda ortaya çıkar. İşlevsel Hilbert uzay sayesinde tanımlanan Berezin dönüşümü ise, düzgün fonksiyonları analitik fonksiyonların Hilbert ...
Mehmet Gürdal, Hamdullah Başaran
doaj   +2 more sources

Longitudinal Single-Axon-Resolution Imaging of Peripheral Nerve Injury Response in Mice Using an Optical Window Implant. [PDF]

Adv Sci (Weinh)
A minimally invasive optical window enables stable, long‐term imaging of peripheral nerves in vivo at single‐axon resolution. Dynamic processes of degeneration, regeneration, and cellular remodeling are visualized across multiple time scales within the same nerve region, providing a unique platform to study a variety of anatomical and molecular events ...
Luzhansky ID, Anisman E, Perez R, Zhang S, Hoffman M, Hunter D, Cherian A, Bonner J, Feria E, Ahmed A, Malik M, Du J, Sudlow LC, Brogan DM, Wood MD, Berezin MY.   +15 more
europepmc   +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

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

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