Search results for "BESS"

Fourier analysis of periodic Radon transforms

2019

We study reconstruction of an unknown function from its $d$-plane Radon transform on the flat $n$-torus when $1 \leq d \leq n-1$. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We solve the associated Tikhonov minimization problem on $H^s$ Sobolev spaces using the properties of the adjoint and normal operators. One of the inversion formulas implies that a compactly supported distribution on the plane with zero average is a weighted sum of its X-ray data.

New special function recurrences giving new indefinite integrals

2018

ABSTRACTSequences of new recurrence relations are presented for Bessel functions, parabolic cylinder functions and associated Legendre functions. The sequences correspond to values of an integer variable r and are generalizations of each conventional recurrence relation, which correspond to r=1. The sequences can be extended indefinitely, though the relations become progressively more intricate as r increases. These relations all have the form of a first-order linear inhomogeneous differential equation, which can be solved by an integrating factor. This gives a very general indefinite integral for each recurrence. The method can be applied to other special functions which have conventional …

Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

2015

We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.

Frames and representing systems in Fréchet spaces and their duals

2014

[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.

Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces

2016

Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every \(\omega \)-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrodinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.

Zvaigžņotā Debess: 2020/2021, Ziema (250)

2021

Zvaigžņotā Debess: 2021, Pavasaris (251)

2021

Zvaigžņotā Debess: 2006, Rudens

2006

Latvijas Zinātņu akadēmija, Latvijas Universitāte

Sesquilinear forms associated to sequences on Hilbert spaces

2019

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.

Assessing the Economic Benefit due to BESS Management in a Renewable Energy Community of a Small Island

2022

The paper presents a study carried out on the island of Pantelleria regarding the interaction among distributed energy resource and energy storage systems in renewable energy communities. EU, in the Clean Energy Package, defines the 'Jointly acting renewables self-consumers' (JARSCs) and the 'Renewable Energy Communities' (RECs) as innovative models to share energy from renewables facilities. Nevertheless, the behaviour of JARSCs and RECs is designed to maximize the final users' self-consumption without considering the impacts on the power grid operation. A comparison of various operational strategies of BESS and an investigation of their effect on the distribution network are key elements …