Cited By
View all- Abramov SPogudin G(2025)On the dimension of the solution space of linear difference equations over the ring of infinite sequencesJournal of Symbolic Computation10.1016/j.jsc.2024.102350127(102350)Online publication date: Mar-2025
Linear Difference Operators with Sequence Coefficients Having Infinite-Dimentional Solution Spaces
Pages 1 - 4
Abstract
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite-dimensionality of its space VL of solutions belonging to R is the presence of a lacunary sequence in VL.
References
[1]
S. Abramov, M.A. Barkatou, M. Petkovsek. Linear difference operators with coeffcients in the form of infnite sequences. Computational Mathematics and Mathematical Physics, 2021, Vol. 61, No. 10, pp. 1582--1589.
[2]
A. Ovchinnikov, G. Pogudin, T. Scanlon. Effective difference elimination and Nullstellensatz. Journal of European Mathematical Society, 2020, Vol. 22, No. 8, pp. 2419--2452
[3]
G. Pogudin, T. Scanlon, M. Wibmer. Solving difference equations in sequences: Universality and Undecidability. Forum of Mathematics, Sigma, 2020, Vol. 8, e33.
[4]
M. Wibmer, On the dimension of systems of algebraic difference equations. Advances in Applied Mathematics, 2021, Vol. 123.
Recommendations
Lacunary difference ideal convergent sequence spaces of fuzzy numbers
In this article, using the Orlicz function M and the difference operator of order n ≥ 1, we introduce the spaces of lacunary ideal convergent difference sequences and lacunary strongly summable difference sequences of fuzzy numbers via fuzzy metric. We ...
Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequences
In this paper we introduce and examine some properties of the sequence spaces C(@D"v^m,@q,(p)),C[@D"v^m,@q,(p)],C"~(@D"v^m,@q,(p)),C"~[@D"v^m,@q,(p)],N"@q(@D"v^m,(p)),S"@q(@D"v^m) and study various properties and inclusion relations of these spaces. We ...
Lacunary strong A-convergence with respect to a sequence of modulus functions
The definition of lacunary strong A-convergence with respect to a modulus is extended to a definition of lacunary strong A-convergence with respect to a sequence of modulus functions. We study some connections between lacunary strong A-convergence with ...
Comments
Information & Contributors
Information
Published In
Copyright © 2023 Copyright is held by the owner/author(s).
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 19 July 2023
Published in SIGSAM-CCA Volume 57, Issue 1
Check for updates
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 21Total Downloads
- Downloads (Last 12 months)10
- Downloads (Last 6 weeks)1
Reflects downloads up to 21 Oct 2024
Other Metrics
Citations
Cited By
View all- Abramov SPogudin G(2025)On the dimension of the solution space of linear difference equations over the ring of infinite sequencesJournal of Symbolic Computation10.1016/j.jsc.2024.102350127(102350)Online publication date: Mar-2025
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in