Results 11 to 20 of about 184 (106)

Stability in Generalized Functions [PDF]

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
doaj   +3 more sources

Asymptotic hyperfunctions, tempered hyperfunctions, and asymptotic expansions [PDF]

International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 5, Page 755-788, 2005., 2022
S.755-788We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory.
Schmidt, A.U.
core   +5 more sources

Fourier transformation of Sato's hyperfunctions [PDF]

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.
Smirnov, A.G.
openaire   +4 more sources

Structure of the extended Fourier hyperfunctions [PDF]

Japanese journal of mathematics. New series, 1993
\textit{T. Matsuzawa's} Methode zur Beschreibung der Struktur von Räumen von Distributionen, Ultradistributionen und Hyperfunktionen [Trans. Am. Math. Soc. 313, No. 2, 619-654 (1989; Zbl 0681.46042)] wird hier zur Strukturbeschreibung des Raumes \({\mathcal G}'\) von erweiterten Fourier Hyperfunktionen verwendet. Es wird gezeigt, daß jedes \(u\) in \({\
CHUNG, Soon-Yeong, KIM, Dohan, KIM, Sung Ki   +2 more
openaire   +4 more sources

Supershift properties for nonanalytic signals. [PDF]

Nanophotonics
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
Colombo F, Sabadini I, Struppa DC, Yger A.   +3 more
europepmc   +2 more sources

Schwartz kernel theorem for the Fourier hyperfunctions [PDF]

Tsukuba Journal of Mathematics, 1995
The purpose of this paper is to give a direct proof of the Schwartz kernel theorem for the Fourier hyperfunctions. The Schwartz kernel theorem for the Fourier hyperfunctions means that with every Fourier hyperfunction \(K\) in \({\mathcal F}(\mathbb{R}^{n_1}\times \mathbb{R}^{n_2})\) we can associate a linear map \[ {\mathcal K}:{\mathcal F}(\mathbb{R}^
Chung, Soon-Yeon, Kim, Dohan, Lee, Eun Gu   +2 more
openaire   +4 more sources

Support and kernel theorem for Fourier hyperfunctions [PDF]

Osaka Journal of Mathematics, 2001
The existence and the characterization of the support of a Fourier hyperfunction \(u\) is not trivial; the support can contain or consists of infinite points. By definition, if \(u\) is a Fourier hyperfunction \((u\in Q' (\mathbb{D}^n)\), \(\mathbb{D}^n= \mathbb{R}^n\cup S^{n-1})\) and if it can be identified by an element of \(Q'(K)\), where \(K\) is ...
Nishimura, Takeshi, Nagamachi, Shigeaki
openaire   +6 more sources

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

[Retracted] Cellular Imaging Analysis Algorithm‐Based Assessment and Prediction of Disease in Patients with Acute Lung Injury

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, Chengwang Xiao, Taoyi Cheng, Zhaohan Wang, Wenhan Xia, Yuvaraja Teekaraman   +5 more
wiley   +1 more source

Vector-valued Fourier hyperfunctions and boundary values [PDF]

This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrizable locally convex Hausdorff space E.
Kruse, Karsten; id_orcid
core   +5 more sources