Jacek Gulgowski
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View article: Compactness in spaces of functions of bounded variation from ideal perspective
Compactness in spaces of functions of bounded variation from ideal perspective Open
Recently we have presented a unified approach to two classes of Banach spaces defined by means of variations (Waterman spaces and Chanturia classes), utilizing the concepts from the theory of ideals on the set of natural numbers. We define…
View article: Compactness in spaces of functions of bounded variation from ideal perspective
Compactness in spaces of functions of bounded variation from ideal perspective Open
Recently we have presented a unified approach to two classes of Banach spaces defined by means of variations (Waterman spaces and Chanturia classes), utilizing the concepts from the theory of ideals on the set of natural numbers. We define…
View article: Functions of bounded variation from ideal perspective
Functions of bounded variation from ideal perspective Open
We present a unified approach to two classes of Banach spaces defined with the aid of variations: Waterman spaces and Chanturia classes. Our method is based on some ideas coming from the theory of ideals on the set of natural numbers.
View article: Compactness in the spaces of functions of bounded variation
Compactness in the spaces of functions of bounded variation Open
Recently, the characterization of the compactness in the space \mathrm{BV}([0,1]) of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman \L…
View article: Properties of local orthonormal systems Part I: Unconditionality in Lp$L^p$, 1<p<∞$1&lt;p&lt;\infty$
Properties of local orthonormal systems Part I: Unconditionality in Lp$L^p$, 1<p<∞$1<p<\infty$ Open
Assume that we are given a filtration on a probability space of the form that each is generated by the partition of one atom of into two atoms of having positive measure. Additionally, assume that we are given a finite‐dimensional linear s…
View article: Properties of local orthonormal systems, Part III: Variation spaces
Properties of local orthonormal systems, Part III: Variation spaces Open
In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best $n$-term piecewise polynomial approximation spaces as real interpolation spaces between $L^p$ and some spaces of bounded dya…
View article: Integral operators in the spaces of functions of bounded Schramm variation
Integral operators in the spaces of functions of bounded Schramm variation Open
In this paper we provide a full characterization of linear integral operators acting from the space of functions of bounded Jordan variation to the space of functions of bounded Schramm variation in terms of their generating kernels.
View article: FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations Open
In this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive…
View article: Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton
Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton Open
We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg–Richter law and Omori law with the wait…
View article: Properties of local orthonormal systems, Part II: Geometric characterization of Bernstein inequalities
Properties of local orthonormal systems, Part II: Geometric characterization of Bernstein inequalities Open
Let $(Ω,\mathscr F,\mathbb P) $ be a probability space and let $(\mathscr F_n)$ be a binary filtration, i.e. exactly one atom of $\mathscr F_{n-1}$ is divided into two atoms of $\mathscr F_n$ without any restriction on their respective mea…
View article: Properties of local orthonormal systems, Part I: Unconditionality in $L^p, 1
Properties of local orthonormal systems, Part I: Unconditionality in $L^p, 1 Open
Assume that we are given a filtration $(\mathscr F_n)$ on a probability space $(Ω,\mathscr F,\mathbb P)$ of the form that each $\mathscr F_n$ is generated by the partition of one atom of $\mathscr F_{n-1}$ into two atoms of $\mathscr F_n$ …
View article: Compactness in Lipschitz spaces and around
Compactness in Lipschitz spaces and around Open
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/Hölder continuous mappings from an arbitrary (not necessarily compact) metric space to a normed space. To this end some extensions and generalizations of e…
View article: Compactness in the spaces of functions of bounded variation
Compactness in the spaces of functions of bounded variation Open
Recently the characterization of the compactness in the space $BV([0,1])$ of functions of bounded Jordan variation was given. Here, certain generalizations of this result are given for the spaces of functions of bounded Waterman $Λ$-variat…
View article: Compactness in Lipschitz spaces and around
Compactness in Lipschitz spaces and around Open
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/Hölder continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compac…
View article: Analytical Methods for Causality Evaluation of Photonic Materials
Analytical Methods for Causality Evaluation of Photonic Materials Open
We comprehensively review several general methods and analytical tools used for causality evaluation of photonic materials. Our objective is to call to mind and then formulate, on a mathematically rigorous basis, a set of theorems which ca…
View article: Generalized Dold Sequences on Partially-Ordered Sets
Generalized Dold Sequences on Partially-Ordered Sets Open
Dold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets…
View article: Compactness in normed spaces: a unified approach through semi-norms
Compactness in normed spaces: a unified approach through semi-norms Open
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural condition…
View article: Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector Open
In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact…
View article: Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative
Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative Open
In this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to …
View article: On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory Open
In this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. P…
View article: On the characterization of compactness in the space of functions of bounded variation in the sense of Jordan
On the characterization of compactness in the space of functions of bounded variation in the sense of Jordan Open
The main goal of this paper is to prove a compactness criterion for subsets of the Banach space of functions of bounded variation in the sense of Jordan. In comparison to the compactness criterion contained in Dunford–Schwartz's monograph,…
View article: Bounded variation solutions to Sturm-Liouville problems
Bounded variation solutions to Sturm-Liouville problems Open
In this article we consider singular Sturm-Liouville problems whose right-hand side is a function of bounded Jordan variation. We present necessary and sufficient conditions for all solutions to be of bounded Jordan variation.
View article: On some nonlinear operators in $${\varvec{\Lambda }} {\varvec{BV}}$$ Λ B V -spaces
On some nonlinear operators in $${\varvec{\Lambda }} {\varvec{BV}}$$ Λ B V -spaces Open
In this paper we investigate autonomous as well as nonautonomous superposition operators acting between spaces of functions of bounded $$\Lambda $$ -variation. A particular emphasis is put on acting conditions as well as on continuity prob…
View article: On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation
On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation Open
In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded variation, namely the problem concerning their continuity. We basically consider autonom…