In this paper, some basic results and notations related to Lebedev- Skalskaya transforms (LS-transforms) are introduced and then estimates of translation and convolution operators associated to LS-transform are obtain...
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In this paper, some basic results and notations related to Lebedev- Skalskaya transforms (LS-transforms) are introduced and then estimates of translation and convolution operators associated to LS-transform are obtained. Continuity of LS-transforms on Lebesgue space as well as on function spaces S-beta,S-k and G(alpha,k) are discussed. Pseudo-differential operators in terms of LS-transforms are defined and their integral representations have been studied in various ways. Moreover, their estimates in Lebesgue space are obtained. At the end, some applications have been discussed.
In this paper we study nonlinear diameter preserving mappings defined between function spaces and obtain generalizations of, basically, all known results concerning diameter preservers. In particular, we give a comple...
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In this paper we study nonlinear diameter preserving mappings defined between function spaces and obtain generalizations of, basically, all known results concerning diameter preservers. In particular, we give a complete description for algebras of continuously differentiable functions, (little) Lipschitz algebras and dense function spaces.
We establish that an uncountable space X must be essentially uncountable whenever its extent and tightness are countable. As a consequence, the equality ext(X)=t(X)=omega$$\mathrm{ext}(X)= t(X)=\omega $$\end{document}...
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We establish that an uncountable space X must be essentially uncountable whenever its extent and tightness are countable. As a consequence, the equality ext(X)=t(X)=omega$$\mathrm{ext}(X)= t(X)=\omega $$\end{document} implies that the space Cp(X,[0,1]) is discretely selective. If X is a metrizable space, then Cp(X,[0,1])has the Banakh property if and only if so does Cp(Y,[0,1]) for some closed separable Y subset of XWe apply the above results to show that, for a metrizable X, the space Cp(X,[0,1])is strongly dominated by a second countable space if and only if X is homeomorphic to D circle plus M where D is a discrete space and M is countable. For a metrizable space X, we also prove that Cp(X,[0,1])has the Lindelof sigma-property if and only if the set of non-isolated points of X is second countable. Our results solve several open questions.
Historically the qualification process for vehicles carrying vulnerable components has centered around the Shock Response Spectrum (SRS) and qualification consisted of devising a collection of tests whose collective S...
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ISBN:
(纸本)9783030126766;9783030126759
Historically the qualification process for vehicles carrying vulnerable components has centered around the Shock Response Spectrum (SRS) and qualification consisted of devising a collection of tests whose collective SRS enveloped the qualification SRS. This involves selecting whatever tests are convenient that will envelope the qualification SRS over at least part of its spectrum;this selection is without any consideration of the details of structural response or the nature of anticipated failure of its components. It is asserted that this approach often leads to over-testing, however, as has been pointed out several times in the literature, this approach may not even be conservative. Given the advances in computational and experimental technology in the last several decades, it would be appropriate to seek some strategy of test selection that does account for structural response and failure mechanism and that pushes against the vulnerabilities of that specific structure. A strategy for such a zemblanic (zemblanity is the opposite of serendipity, the faculty of making unhappy, unlucky and expected discoveries by design) approach is presented.
For certain property R of topological T-0-spaces, we prove that if T-0-space Y has property R, then [X, Y] endowed with the Isbell topology possesses R for any T-0-space X;and if [X, Y] has property It for some non-em...
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For certain property R of topological T-0-spaces, we prove that if T-0-space Y has property R, then [X, Y] endowed with the Isbell topology possesses R for any T-0-space X;and if [X, Y] has property It for some non-empty space X, then so does Y. (C) 2021 Elsevier B.V. All rights reserved.
A brief survey of results on the characterization of the spaces associated with given classes of function spaces is presented. It is shown that the situation differs in general for ideal and non-ideal spaces. In the s...
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A brief survey of results on the characterization of the spaces associated with given classes of function spaces is presented. It is shown that the situation differs in general for ideal and non-ideal spaces. In the second case the notion of associated space splits into two. In the main body of the text a complete description is given of the function spaces associated with weighted Sobolev spaces of the first order on the real line.
We extend known results of selection principles in C-p-theory to the context of spaces of the form C-B(X), where B is a bornology on X. Particularly, by using the filter approach of Jordan to C-p-theory, we show that ...
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We extend known results of selection principles in C-p-theory to the context of spaces of the form C-B(X), where B is a bornology on X. Particularly, by using the filter approach of Jordan to C-p-theory, we show that gamma-productive spaces are productive with a larger class of gamma-like spaces. (C) 2019 Elsevier B.V. All rights reserved.
A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of c...
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A separable space is strongly sequentially separable if, for each countable dense set, every point in the space is a limit of a sequence from the dense set. We consider this and related properties, for the spaces of continuous and Borel real-valued functions on Tychonoff spaces, with the topology of pointwise convergence. Our results solve a problem stated by Gartside, Lo, and Marsh. (C) 2019 Elsevier B.V. All rights reserved.
In the present paper we recall the main points of the Fourier Transform developments, in particular the historical origin of the inversion formula. Hence we construct explicit examples of functions in different zones ...
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In the present paper we recall the main points of the Fourier Transform developments, in particular the historical origin of the inversion formula. Hence we construct explicit examples of functions in different zones of the range of the Fourier transform in L-1. These can be used as exercises in a basic course of signal processing or harmonic analysis.
Fractal interpolation functions are fixed points of contraction maps on suitable function spaces. In this paper, we introduce the Kantorovich-Bernstein alpha-fractal operator in the Lebesgue space & 1d4db;(p)(I), ...
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Fractal interpolation functions are fixed points of contraction maps on suitable function spaces. In this paper, we introduce the Kantorovich-Bernstein alpha-fractal operator in the Lebesgue space & 1d4db;(p)(I), 1 <= p <= infinity. The main aim of this article is to study the convergence of the sequence of Kantorovich-Bernstein fractal functions towards the original functions in & 1d4db;(p)(I) spaces and Lipschitz spaces without affecting the non-linearity of the fractal functions. In the first part of this paper, we introduce a new family of self-referential fractal & 1d4db;(p)(I) functions from a given function in the same space. The existence of a Schauder basis consisting of self-referential functions in & 1d4db;(p) spaces is proven. Further, we derive the fractal analogues of some & 1d4db;(p)(I) approximation results, for example, the fractal version of the classical Muntz-Jackson theorem. The one-sided approximation by the Bernstein alpha-fractal function is developed.
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