Results 21 to 30 of about 240 (131)
Stability in Generalized Functions
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We consider the following additive functional equation with n‐independent variables: f(∑i=1nxi)=∑i=1nf(xi)+∑i=1nf(xi-xi-1) in the spaces of generalized functions. Making use of the heat kernels, we solve the general solutions and the stability problems of the above equation in the spaces of tempered distributions and Fourier hyperfunctions.
Young-Su Lee, Dumitru Baleanu
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Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 5, Page 755-788, 2005., 2005 We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these asymptotic and tempered hyperfunctions to known classes of test functions and distributions, especially the Gel′fand‐
Andreas U. Schmidt
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A uniqueness theorem for Boehmians of analytic type
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 7, Page 501-504, 2000., 2000 The following uniqueness theorem is proven for a class of generalized functions. If F is a Boehmian of analytic type and F = 0 on some open arc Ω, then F ≡ 0.
Dennis Nemzer
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VIEW, Volume 7, Issue 1, February 2026.Notes: Their molecular characteristics—such as IDH genotype, P53 phenotype, and Ki‐67 labeling index—are critical determinants of treatment strategies and prognosis for patients of adult‐type diffuse gliomas. In this study, we employed 7‐tesla sodium magnetic resonance imaging (23Na MRI) and demonstrated that total sodium concentration (TSC) and ...
Letian Yuan +9 more
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International Journal of Stochastic Analysis, Volume 11, Issue 1, Page 43-58, 1998., 1997 In this paper, we propose a generalization of continuous‐time processed defined by , to the case of f being a distribution. We give a necessary and sufficient condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to
L. Bel +3 more
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Supershift properties for nonanalytic signals
Nanophotonics, Volume 14, Issue 23, Page 4039-4044, 02 November 2025.Abstract 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
Fabrizio Colombo +3 more
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International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 4, Page 685-692, 1989., 1988 A class of generalized functions, called periodic Boehmians, on the unit circle, is studied. It is shown that the class of Boehmians contain all Beurling distributions. An example of a hyperfunctlon that is not a Boehmian is given. Some growth conditions on the Fourier coefficients of a Boehmian are given.
Dennis Nemzer
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Fourier transformation of Sato's hyperfunctions
Advances in Mathematics, 2005 A new generalized function space in which all Gelfand-Shilov classes $S^{\prime 0}_α$ ($α>1$) of analytic functionals are embedded is introduced. This space of {\it ultrafunctionals} does not possess a natural nontrivial topology and cannot be obtained via duality from any test function space.
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2019 ACVIM Forum Research Abstract Program
, 2019 Journal of Veterinary Internal Medicine, Volume 33, Issue 5, Page 2375-2547, September/October 2019.
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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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