ISSN 1683-3414 (Print)   •   ISSN 1814-0807 (Online)
   Log in
 

Contacts

Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54
E-mail: rio@smath.ru

 

 

 

ßíäåêñ.Ìåòðèêà

Dear authors!
Submission of all materials is carried out only electronically through Online Submission System in personal account.
DOI: 10.46698/j1917-4964-8877-l

Asymptotic Almost Automorphy for Algebras of Generalized Functions

Bouzar, Ch.  , Slimani, M.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 2.
Abstract:
The paper aims to to study the concept of asymptotic almost automorphy in the context of generalized functions. We introduce an algebra of asymptotically almost automorphic generalized functions which contains the space of smooth asymptotically almost automorphic functions as a subalgebra. The fundamental importance of this algebra, is related to the impossibility of multiplication of distributions; it also contains the asymptotically almost automorphic Sobolev-Schwartz distributions as a subspace. Moreover, it is shown that the introduced algebra is stable under some nonlinear operations. As a by pass result, the paper gives a Seeley type result on extension of functions in the context of the algebra of bounded generalized functions and the algebra of bounded generalized functions vanishing at infinity, these results are used to prove the fundamental result on the uniqueness of decomposition of an asymptotically almost automorphic generalized function. As applications, neutral difference-differential systems are considered in the framework of the algebra of generalized functions.
Keywords: asymptotic almost automorphy, generalized functions, neutral difference differential equations.
Language: English Download the full text  
For citation: Bouzar, Ch. and Slimani, M. Asymptotic Almost Automorphy for Algebras of Generalized Functions, Vladikavkaz Math. J., 2023, vol. 25, no. 2, pp. 38-55. DOI 10.46698/j1917-4964-8877-l
+ References


← Contents of issue
 
  | Home | Editorial board | Publication ethics | Peer review guidelines | Latest issue | All issues | Rules for authors | Online submission system’s guidelines | Submit manuscript |  
© 1999-2023 Þæíûé ìàòåìàòè÷åñêèé èíñòèòóò