In the paper, we have pointed out the conditions under which the subspaces of dimensionality $n^2$ ($n=2,3,\ldots$), extremal for $H_{\omega}$ classes of continuous functions of two variables, do not exist.
The paper describes the structure of a linear continuous operator on the space of continuous functions in the topology of pointwise convergence. The corresponding theorem is a generalization of A.V.Arkhangel'skii's theorem on the general form of a continuous linear functional on such spaces.
We obtain two-sided bounds, and, in some cases, exact values as well, for interpolational spreads of subspaces of Hermitian splines in the space of continuous functions with uniform metric.
In this paper, we consider a certain integral operator with a weight, loaded with operator term. It acts in the space of continuous functions. The conditions under which this operator is limited are determined, the form of its semigroup is es-tablished. The Cauchy problem for an integro-differential equation is considered as an application. Such equations arise in the theory of elasticity and models of biological processes: Proctor's problem on the equilibrium of an elastic beam, Volterra's problem on torsional vibrations, Prandtl's problem for calculating an airplane wing, in analysis of economic models, etc.
AbstractIn this work we study the Ulam–Hyers stability of a differential equation. Its proof is based on the Banach fixed point theorem in some space of continuous functions equipped with the norm $\|\cdot \|_{\infty }$
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AbstractAccording to the famous and pioneering result of Laurent Schwartz, any closed translation invariant linear space of continuous functions on the reals is synthesizable from its exponential monomials. Due to a result of D. I. Gurevič there is no straightforward extension of this result to higher dimensions. Following Székelyhidi (Acta Math Hungar 153(1):120–142, 2017), with the aid of Gelfand pairs and K-spherical functions, K-synthesizability of K-varieties can be described. In this paper we contribute to this direction in the special case when K is the symmetric group of order d.
In this paper, we mainly discuss continuous functions with certain fractal dimensions on [Formula: see text]. We find space of continuous functions with certain Box dimension is not closed. Furthermore, Box dimension of linear combination of two continuous functions with the same Box dimension maybe does not exist. Definitions of fractal functions and local fractal functions have been given. Linear combination of a fractal function and a local fractal function with the same Box dimension must still be the original Box dimension with nontrivial coefficients.
Extremal subspaces in the problem about widths of $H_{\omega}$ classes in the space of continuous functions of two variables
