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Metric Spaces A Companion to Analysis
This textbook presents the theory of Metric Spacesnecessary for studying analysis beyond one real variable. Rich in examples, exercises and...
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Essential Ordinary Differential Equations
This textbook offers an engaging account of the theory of ordinary differential equations intended for advanced undergraduate students of...
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Coincidence and Fixed Points of Set-Valued Map**s Via Regularity in Metric Spaces
In this paper, we construct a common iterative scheme that allows to unify two important results established recently by Ioffe and Ait Mansour,...
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Metric Spaces and Manifolds
Metrics quantify the difference between points in a symmetric manner. Many data arise with such a structure, and metric geometry, therefore is a...
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On General Solutions of Sinyukov Equations on Two-Dimensional Equidistant (pseudo-)Riemannian Spaces
The paper is devoted to study of Sinyukov equations on two-dimensional equidistant (pseudo-) Riemannian spaces. The general solution of Sinyukov...
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On Representations of Groups and Algebras in Spaces with Indefinite Metric
The paper contains a survey of known results on the structure of J -symmetric operator algebras in Pontryagin and Krein spaces, as well as on...
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Polylinear Differential Realization of Deterministic Dynamic Chaos in the Class of Higher Order Equations with Delay
AbstractA characteristic criterion (and its modifications) of the solvability of differential realization of the bundle of controlled trajectory...
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Weighted Fractional Hardy Operators and their Commutators on Generalized Morrey Spaces over Quasi-Metric Measure Spaces
We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure...
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The Dirichlet Problem for p-minimizers on Finely Open Sets in Metric Spaces
We initiate the study of fine p -(super)minimizers, associated with p -harmonic functions, on finely open sets in metric spaces, where
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Complement: Elements of the Theory of Ordinary Differential Equations
In this chapter we introduce the elementary theory of dynamical systems in terms of systems of ordinary differential equations, also on...
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Mobility Spaces
In this paper, we consider generalizations of the Galilean space endowed with an action of a nonlinear transformation group. We prove that such...
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Differential equations and Lie group representations
We discuss the role of differential equations in Lie group representation theory. We use Kashiwara’s pentagon as a reference frame for the real...
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Theory and methods for random differential equations: a survey
In this survey, we present an overview of random differential equations, focusing on strong solutions and methods for estimation of statistics and...
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From Strichartz Estimates to Differential Equations on Fractals
Robert Strichartz made a substantial impact on analysis via his deep and original results in classical harmonic, functional, and spectral analysis...
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The Differential Equations in Euler’s Work on Geography
We present Euler’s method for the construction of geographical projections. In particular, we explain how Euler translated natural hypotheses on...
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Short Essay on Difference Equations with Continuous Argument
The aim of the present paper is to draw attention to difference equations with continuous argument, which are paradigmatic for the simulation of...
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Compact Spaces
Motivates and defines the key concept of compactness. The high point is the equivalence, for metric spaces, of compactness and sequential...
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Scalable spaces
Scalable spaces are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat)...
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Random Processes on Non-Archimedean Spaces
The Lévy stochastic processes on p-adic numbers have been constructed by different methods. We present the construction by Albeverio and Karwowski...