Mathematics

Journal Browser

► Journal Browser

Advances in Complex Analysis and Its Applications in Operator Theory, Functional and Noncommutative Analysis

Share This Special Issue

Special Issue Editor

Prof. Dr. Danko R. Jocić

E-Mail Website
Guest Editor

Department of Mathematics, University of Belgrade, 105104 Belgrade, Serbia
Interests: transformers in operator theory and matrix analysis; operator and norm inequalities; Bloch and weighted Lipschitz spaces; Bergman spaces in model theory for operators

Special Issue Information

Dear Colleagues,

Complex analysis is a very prosperous and inseparable part of mathematical analysis. Its traditional focus in on functions with one or several complex variables, especially those that are holomorphic in their domains. Cauchy and other representation formulas for holomorphic functions give rise to functional calculus with one or several operators (as variables), leading to the development of Cauchy–Dunford, Nagy–Foias, Taylor and spectral functional calculus.

Fourier and Laplace transforms are not just an important topic in mathematical analysis and other branches of mathematics and engineering, but also play a significant role in some Banach spaces of analytic functions, including, amongst others, Hardy, Bergman and Paley—Wiener spaces.

This Special Issue intends to present recent results and developments on the Banach spaces of complex and vector-valued functions, Fourier and Laplace transforms and transformers, and elementary and Birman–Solomyak transformers, which are given by double operator integrals on the ideals of compact operators, with applications in operator and norm inequalities. Also, works on the progress of functional calculus with several operators, model operators and model spaces, and its applications, will be welcomed in this Special Issue.

Prof. Dr. Danko R. Jocić
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Benefits of Publishing in a Special Issue

Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.

Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.

Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.

External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.

e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (1 paper)

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

14 pages, 337 KiB

Open AccessArticle

Norm Estimates for Remainders of Noncommutative Taylor Approximations for Laplace Transformers Defined by Hyperaccretive Operators

by Danko R. Jocić

Mathematics 2024, 12(19), 2986; https://doi.org/10.3390/math12192986 - 25 Sep 2024

Viewed by 753

Abstract

Let

H

be a separable complex Hilbert space,

B (H)

the algebra of bounded linear operators on

H

μ

a finite Borel measure on

R_{+}

with the finite

(n + 1)

-th moment, [...] Read more.

Let

H

be a separable complex Hilbert space,

B (H)

the algebra of bounded linear operators on

H

μ

a finite Borel measure on

R_{+}

with the finite

(n + 1)

-th moment,

f (z) : = \int_{R_{+}} e^{- t z} d μ (t)

for all

ℜ z ⩾ 0, C_{Ψ} (H)

, and

| | \cdot {| |}_{Ψ}

the ideal of compact operators and the norm associated to a symmetrically norming function

Ψ,

respectively. If

A, D \in B (H)

are accretive, then the Laplace transformer on

B (H),

X \mapsto \int_{R_{+}} e^{- t A} X e^{- t D} d μ (t)

is well defined for any

X \in B (H)

as is the newly introduced Taylor remainder transformer

R_{n} (f; D, A) X : = f (A) X - \sum_{k = 0}^{n} \frac{1}{k!} \sum_{i = 0}^{k} {(- 1)}^{i} (\binom{k}{i}) A^{k - i} X D^{i} f^{(k)} (D) .

A, D^{*}

are also

(n + 1)

-accretive,

\sum_{k = 0}^{n + 1} {(- 1)}^{k} (\binom{n + 1}{k}) A^{n + 1 - k} X D^{k} \in C_{Ψ} (H)

and

| | \cdot {| |}_{Ψ}

is Q* norm, then

| | \cdot {| |}_{Ψ}

norm estimates for

{(\sum_{k = 0}^{n + 1} (\binom{n + 1}{k}) A^{k} A^{n + 1 - k})}^{\frac{1}{2}} R_{n} (f; D, A) X {(\sum_{k = 0}^{n + 1} (\binom{n + 1}{k}) D^{n + 1 - k} D^{* k})}^{\frac{1}{2}}

are obtained as the spacial cases of the presented estimates for (also newly introduced) Taylor remainder transformers related to a pair of Laplace transformers, defined by a subclass of accretive operators. Full article

(This article belongs to the Special Issue Advances in Complex Analysis and Its Applications in Operator Theory, Functional and Noncommutative Analysis)

Show export options Show export options

Select all

Export citation of selected articles as:

Displaying articles 1-1

Journal Menu

Journal Browser

Advances in Complex Analysis and Its Applications in Operator Theory, Functional and Noncommutative Analysis

Share This Special Issue

Special Issue Editor

Special Issue Information

Benefits of Publishing in a Special Issue

Published Papers (1 paper)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI