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Functional Analysis, Topology and Quantum Mechanics II

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (30 March 2023) | Viewed by 6545

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Special Issue Editors

Prof. Dr. Rafael de la Rosa

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Guest Editor

Department of Mathematics, University of Cádiz, Puerto Real, Cadiz 11003, Spain
Interests: Lie symmetries; partial differential equations; Nonlocal symmetries
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Francisco Javier Garcia-Pacheco

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Department of Mathematics, College of Engineering, Universidad de Cádiz, 11510 Puerto Real, Spain
Interests: functional analysis; algebra; geometry; topology
Special Issues, Collections and Topics in MDPI journals

Dr. Adrián Ruiz Serván

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Departamento de Matemáticas, Escuela de Ingenierías Marina, Náutica y Radioelectrónica, Universidad de Cádiz, 11510 Puerto Real, Spain
Interests: mathematical analysis; Lie symmetries; Differential equations

Special Issue Information

The scope of this Special Issue deals with the strong interaction between the operator theory and the geometry of Banach spaces and topological vector spaces. Applications of the two aforementioned theories to quantum systems are very welcome.

Prof. Dr. Rafael de la Rosa
Prof. Francisco Javier Garcia-Pacheco
Dr. Adrián Ruiz Serván
Guest Editors

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.

Keywords

Banach spaces and algebras
Hilbert spaces
Selfadjoint operator
Convexity and smoothness
Algebras of continuous functions
Measure spaces
Effect algebras
Series and summability
Quantum systems
Probability density operator
Unbounded observables

Related Special Issue

Functional Analysis, Topology and Quantum Mechanics, 3rd Edition in Mathematics

Published Papers (5 papers)

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Research

10 pages, 427 KiB

Open AccessArticle

Asymptotic ω-Primality of Finitely Generated Cancelative Commutative Monoids

by Juan Ignacio García-García, Daniel Marín-Aragón and Alberto Vigneron-Tenorio

Mathematics 2023, 11(4), 790; https://doi.org/10.3390/math11040790 - 04 Feb 2023

Viewed by 1200

Abstract

The computation of

ω

-primality has been object of study, mainly, for numerical semigroups due to its multiple applications to the Factorization Theory. However, its asymptotic version is less well known. In this work, we study the asymptotic

ω

-primality for finitely generated [...] Read more.

The computation of

ω

ω

-primality for finitely generated cancelative commutative monoids. By using discrete geometry tools and the Python programming language we present an algorithm to compute this parameter. Moreover, we improve the proof of a known result for numerical semigroups. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics II)

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Figure 1

12 pages, 286 KiB

Open AccessArticle

Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs

by Hani Abdelwahab, Elisabete Barreiro, Antonio J. Calderón and José M. Sánchez

Mathematics 2023, 11(3), 725; https://doi.org/10.3390/math11030725 - 01 Feb 2023

Viewed by 1036

Abstract

In this work, we study a linear operator f on a pre-Euclidean space

V

by using properties of a corresponding graph. Given a basis

B

V

, we present a decomposition of

V

as an orthogonal direct sum of certain linear subspaces [...] Read more.

In this work, we study a linear operator f on a pre-Euclidean space

V

by using properties of a corresponding graph. Given a basis

B

V

, we present a decomposition of

V

as an orthogonal direct sum of certain linear subspaces

{U_{i}}_{i \in I}

, each one admitting a basis inherited from

B

, in such way that

f = \sum_{i \in I} f_{i}

. Each

f_{i}

is a linear operator satisfying certain conditions with respect to

U_{i}

. Considering this new hypothesis, we assure the existence of an isomorphism between the graphs of f relative to two different bases. We also study the minimality of

V

by using the graph of f relative to

B

. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics II)

13 pages, 311 KiB

Open AccessFeature PaperArticle

On Focal Borel Probability Measures

by Francisco Javier García-Pacheco, Jorge Rivero-Dones and Moisés Villegas-Vallecillos

Mathematics 2022, 10(22), 4365; https://doi.org/10.3390/math10224365 - 20 Nov 2022

Cited by 1 | Viewed by 1192

Abstract

The novel concept of focality is introduced for Borel probability measures on compact Hausdorff topological spaces. We characterize focal Borel probability measures as those Borel probability measures that are strictly positive on every nonempty open subset. We also prove the existence of focal Borel probability measures on compact metric spaces. Lastly, we prove that the set of focal (regular) Borel probability measures is convex but not extremal in the set of all (regular) Borel probability measures. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics II)

16 pages, 280 KiB

Open AccessFeature PaperArticle

Some Generalized Versions of Chevet–Saphar Tensor Norms

by Ju Myung Kim

Mathematics 2022, 10(15), 2716; https://doi.org/10.3390/math10152716 - 01 Aug 2022

Viewed by 983

Abstract

The paper is concerned with some generalized versions

g_{E}

and

w_{E}

of classical tensor norms. We find a Banach space E for which

g_{E}

and

w_{E}

are finitely generated tensor norms, and show that

g_{E}

and

w_{E}

[...] Read more.

The paper is concerned with some generalized versions

g_{E}

and

w_{E}

of classical tensor norms. We find a Banach space E for which

g_{E}

and

w_{E}

are finitely generated tensor norms, and show that

g_{E}

and

w_{E}

are associated with the ideals of some E-nuclear operators. We also initiate the study of some theories of our tensor norms. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics II)

18 pages, 381 KiB

Open AccessFeature PaperArticle

Analytical Solutions to Minimum-Norm Problems

by Almudena Campos-Jiménez, José Antonio Vílchez-Membrilla, Clemente Cobos-Sánchez and Francisco Javier García-Pacheco

Mathematics 2022, 10(9), 1454; https://doi.org/10.3390/math10091454 - 26 Apr 2022

Cited by 1 | Viewed by 1383

Abstract

For

G \in R^{m \times n}

and

g \in R^{m}

, the minimization

{min ∥ G ψ - g ∥}_{2}

, with

ψ \in R^{n}

, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an [...] Read more.

For

G \in R^{m \times n}

and

g \in R^{m}

, the minimization

{min ∥ G ψ - g ∥}_{2}

, with

ψ \in R^{n}

, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is

min ∥ T (h) - k ∥

, where

T : H \to K

is a continuous linear operator between Hilbert spaces

H, K

and

h \in H, k \in K

. In order to avoid an unbounded set of solutions for the Tykhonov regularization, we transform the infinite-dimensional Tykhonov regularization into a multiobjective optimization problem:

min ∥ T (h) - k ∥ and min ∥ h ∥

. We call it bounded Tykhonov regularization. A Pareto-optimal solution of the bounded Tykhonov regularization is found. Finally, the bounded Tykhonov regularization is modified to introduce the precise Tykhonov regularization:

min ∥ T (h) - k ∥ with ∥ h ∥ = α

. The precise Tykhonov regularization is also optimally solved. All of these mathematical solutions are optimal for the design of Magnetic Resonance Imaging (MRI) coils. Full article

(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics II)

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