Results 1 to 10 of about 101 (82)
Supershift properties for nonanalytic signals. [PDF]
NanophotonicsAbstract The phenomenon of superoscillations is of great interest in microscopy, antenna design, and material sciences. This phenomenon has been generalized and has given rise to the concept of supershift, which is a far reaching extension that applies to functions that may present discontinuous derivatives. From this perspective, this is a notion that
Colombo F +3 more
europepmc +2 more sources
Stability in Generalized Functions
Abstract and Applied Analysis, 2011 We consider the following additive functional equation with 𝑛-independent variables: ∑𝑓(𝑛𝑖=1𝑥𝑖∑)=𝑛𝑖=1𝑓(𝑥𝑖∑)+𝑛𝑖=1𝑓(𝑥𝑖−𝑥𝑖−1) in the spaces of generalized functions.
Young-Su Lee
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CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS
Journal of the Korean Mathematical Society, 2005 The author of this paper defines the convolution of Fourier hyperfunctions and analyses its properties making use of the method given in the book [\textit{S. G. Gindikin} and \textit{L. R. Volevich}, ``Distributions and Convolution Equations'' (Gordon and Breach Sci. Publ.) (1992; Zbl 0760.46029)].
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On localization properties of Fourier transforms of hyperfunctions
Journal of Mathematical Analysis and Applications, 2009 21 pages, final version, accepted for publication in J. Math.
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DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS [PDF]
Bulletin of the Korean Mathematical Society, 2004 Let \(F_{(h,\nu)}\) be the space of differentiable functions \(\varphi(x)\) for which some sup-norm is finite. Then one has the continuous embedding \(F_{(h,\nu)}\subset F_{(h',\nu')}\), \(h\geq h'>0, \nu\geq\nu'\). Let \(\mathcal G=\bigcap_{h,\nu}F_{(h,\nu)}\) be endowed with the natural projective topology.
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Viscosity Limits for Zeroth‐Order Pseudodifferential Operators
Communications on Pure and Applied Mathematics, Volume 75, Issue 8, Page 1798-1869, August 2022., 2022 Abstract Motivated by the work of Colin de Verdière and Saint‐Raymond on spectral theory for zeroth‐order pseudodifferential operators on tori, we consider viscosity limits in which zeroth‐order operators, P, are replaced by P + iν Δ, ν > 0. By adapting the Helffer–Sjöstrand theory of scattering resonances, we show that, in a complex neighbourhood of ...
Jeffrey Galkowski, Maciej Zworski
wiley +1 more source
Stability of Trigonometric Functional Equations in Generalized Functions
Journal of Inequalities and Applications, 2010 We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.
Jeongwook Chang, Jaeyoung Chung
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Contrast Media &Molecular Imaging, Volume 2022, Issue 1, 2022., 2022 This paper uses cellular imaging analysis algorithms to assess and predict the condition of patients with acute lung injury. Given the unique optical properties of UCNPs, this paper designs a ratiometric upconversion fluorescent nanoprobe for the determination of nitric oxide (NO) content in living cells and tissues.
Liang Gao +5 more
wiley +1 more source
Stability of Quartic Functional Equations in the Spaces of Generalized Functions
Advances in Difference Equations, 2009 We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces ...
Chung Soon-Yeong, Lee Young-Su
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Negative Powers of Contractions Having a Strong AA+ Spectrum
Moroccan Journal of Pure and Applied Analysis, 2023 Zarrabi proved in 1993 that if the spectrum of a contraction T on a Banach space is a countable subset of the unit circle 𝕋, and if limn→+∞log(‖T−n‖)n=0{\lim _{n \to + \infty }}{{\log \left( {\left\| {{T^{ - n}}} \right\|} \right)} \over {\sqrt n ...
Esterle Jean
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