可逆正算子的Berezin变换

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2021-01-01 DOI:10.56082/annalsarscimath.2022.1-2.70

N. Das, Madhusmita Sahoo

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引用次数: 0

摘要

本文引入一个类a∧L∞(D)，使得φ∈a满足某正定条件，则存在ψ∈a使得φ(z)≤α ε (z)，对于某常数α > 0。更进一步，如果φ(z) = hAkz, kzi，对于从Bergman空间L2a(D)到自身的有界正可逆算子A，则ψ(z) = h(log A)kz, kzi。其中kz, z∈D是L2a(D)的归一化再现核。本文还讨论了这些结果在非标准生长条件下的应用。我们证明了这个问题至少存在一个弱解。为了做到这一点，主要的工具是用于抽象Hammerstein类型映射的Berkovits度理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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BEREZIN TRANSFORM OF INVERTIBLE POSITIVE OPERATORS

In this paper we introduce a class A ⊂ L∞(D) such that if φ ∈ Aand satisﬁes certain positive-deﬁnite condition, then there exists aψ ∈ A such that φ(z) ≤ αeψ(z), for some constant α > 0. Further,if φ(z) = hAkz, kzi, for some bounded positive, invertible operator Afrom the Bergman space L2a(D) into itself then ψ(z) = h(log A)kz, kzi.Here kz, z ∈ D are the normalized reproducing kernel of L2a(D). Ap-plications of these results are also discusseonly a non-standard growth condition. We show that our problem admits at least one weak solution. In order to do this, the main tool is the Berkovits degree theory for abstract Hammerstein type mappings.

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.