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Anna Rita Sambucini

Publications and source records attributed to Anna Rita Sambucini.

At least 19 recordsLinked to original sources
arXiv2025

The Sturm-Liouville Hierarchy of evolution equations and the Weyl functions of related spectral problems

The goal of the present paper is that of defining the so-called Sturm-Liouville hierarchy of evolution equations, firstly by using the zero-curvature formalism, then by using the asymptotic properties of the Weyl $m$-functions for certain classes of pairs $(q,y)$ of the Sturm-Liouville eigenvalue equation $$-φ''+qφ=λyφ,$$ in the space $L^2(\mathbb R,ydx)$. Since the Weyl $m$-functions are known to contain all the information concerning the spectral properties of the above equation, the determination of the evolution of some spectral characteristics will allow to determine solutions of the hierarchies of evolution equations.

math.CA↗
arXiv2025

Selections of integrable multifunctions in arbitrary Banach spaces

We find the origin of the integration theory for multifunctions in the sixties in the pioneering works of G. Debreu and R. Aumann, Nobel prizes for the Economy in 1983 and in 2005, respectively. The Aumann integral is defined by means the integrals of measurable selections of the multifunctions. An important tool for the existence of measurable selections is the Kuratowski and Ryll-Nardzewski theorem, although this famous result needs the separability of the range space. Other definitions of multifunction integrals, that are not based on selections have been developed such as Pettis, Henstock, McShane, Birkhoff, Kurzweill-Henstock-Pettis, or variationally integrals. However to obtain good properties of such integrals for multifunctions one also needs to study "nice" properties of selections. This chapter is devoted to selection results in the framework of an arbitrary Banach space (non necessarily separable). In particular we address our attention to the existence of selections integrable of the same sense of the given multifunction and to their applications to the problem of representing a multifunction as a translation of a multifunction with better integrable properties by means of one of its integrable selections.

math.FA↗
arXiv2025

Convergence for varying measures

Some limit theorems of the type $\int_Ωf_n dm_n -- --> \int_Ωf dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.

math.FA↗
arXiv2024

Microwave Remote Sensing of Soil Moisture, Above Ground Biomass and Freeze-Thaw Dynamic: Modeling and Empirical Approaches

Human actions have accelerated changes in global temperature, precipitation patterns, and other critical Earth systems. Key markers of these changes can be linked to the dynamic of Essential Climate Variables (ECVs) and related quantities, such as Soil Moisture (SM), Above Ground Biomass (AGB), and Freeze-Thaw (FT) Dynamics. These variables are crucial for understanding global climate changes, hydrological and carbon cycles included. Monitoring these variables helps to validate climate models and inform policy decisions. Technologies like microwave remote sensing provide critical tools for monitoring the effects of human activities on these variables at a global scale. Other than proper tachenological developments, the study of ECVs requires suitable theoretical retrieval tools, which leads to the solutions of inverse problems. In this brief survey, we analyze and summarize the main retrieval techniques available in the literature for SM, AGB, and FT, performed on data collected with microwave remote sensing sensors. Such methods will be some of the fundamental algorithms that can find applications in the research activities of the interdisciplinary, curiosity-driven, project {\it REmote sensing daTa INversion with multivariate functional modeling for essential climAte variables characterization (RETINA)}, recently funded by the European Union under the Italian National Recovery and Resilience Plan of NextGenerationEU, under the Italian Ministry of University and Research. The main goal of RETINA, in which three research units from three different italian universities are involved, is to create innovative techniques for analyzing data generated by the interaction of electromagnetic waves with the Earth's surface, applying theoretical insights to address real-world challenges.

math.NA↗
arXiv2024

A comparison among a fuzzy algorithm for image rescaling with other methods of digital image processing

The aim of this paper is to present a comparison among the fuzzy-type algorithm for image rescaling introduced by Jurio et al., 2011, quoted in the list of references, with some other existing algorithms such as the classical bicubic algorithm and the so-called sampling Kantorovich (SK) one. Note that, the SK algorithm is a recent tool for image rescaling and enhancement that revealed to be useful in several applications to real world problems, while bicubic algorithm is widely known in the literature. The comparison among the above mentioned algorithms (all implemented by MatLab programming language) has been done in term of suitable similarity indexes such as the Peak-Signal-to-Noise-Ratio (PSNR) and the likelihood index $S$. Moreover, also the CPU time of the considered algorithms has been analysed.

math.FA↗
arXiv2023

Representations of multimeasures via multivalued Bartle-Dunford-Schwartz integral

An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the Bartle-Dunford-Schwartz integral with respect to a vector measure presented by Lewis. Its properties are studied together with its application to Radon-Nikodym theorems in order to represent as an integrable derivative the ratio of two general multimeasures or two $d_H$-multimeasures; equivalent conditions are provided in both cases.

math.FA↗
arXiv2022

Some applications of modular convergence in vector lattice setting

The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an integral given in earlier papers.

math.FA↗
arXiv2022

Abstract integration with respect to measures and applications to modular convergence in vector lattice setting

A "Bochner-type" integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties are studied. Moreover, by means of this integral, some convergence results on operators in vector lattice-valued modulars are proved. Some applications are given to moment kernels and to the Brownian motion.

math.FA↗
arXiv2020

Approximation results in Orlicz spaces for sequences of Kantorovich max-product neural network operators

In this paper we study the theory of the so-called Kantorovich max-product neural network operators in the setting of Orlicz spaces $L^φ$. The results here proved, extend those given by Costarelli and Vinti in Result Math., 2016, to a more general context. The main advantage in studying neural network type operators in Orlicz spaces relies in the possibility to approximate not necessarily continuous functions (data) belonging to different function spaces by a unique general approach. Further, in order to derive quantitative estimates in this context, we introduce a suitable K-functional in $L^φ$ and use it to provide an upper bound for the approximation error of the above operators. Finally, examples of sigmoidal activation functions have been considered and studied in details.

math.FA↗
arXiv2020

Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications

In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in the general frame of the Orlicz spaces, which includes as particular case the $L^p$-spaces. Examples of sigmoidal activation functions are discussed, for the above operators in different cases of Orlicz spaces. Finally, concrete applications to real world cases have been presented in both uni-variate and multivariate settings. In particular, the case of reconstruction and enhancement of biomedical (vascular) image has been discussed in details.

math.FA↗
arXiv2020

Some new results on integration for multifunction

It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.

math.FA↗
arXiv2019

Integration of multifunctions with closed convex values in arbitrary Banach spaces

Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We pay particular attention to the "positive multifunctions". Among them an investigation of multifunctions determined by vector-valued functions is presented. Finally, decomposition results are obtained for scalarly and gauge-defined integrals of multifunctions and a full description of McShane integrability in terms of Henstock and Pettis integrability is given.

math.FA↗