SOLVING DIFFERENCE EQUATIONS IN SEQUENCES: UNIVERSALITY AND UNDECIDABILITY

We study solutions of difference equations in the rings of sequences and, more generally, solutions of equations with a monoid action in the ring of sequences indexed by the monoid. This framework includes, for example, difference equations on grids (for example, standard difference schemes) and dif...

Full description

Saved in:
Bibliographic Details
Published inForum of mathematics. Sigma Vol. 8
Main Authors POGUDIN, GLEB, SCANLON, THOMAS, WIBMER, MICHAEL
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 2020
Subjects
03D35
12H10
13P25
14Q20
39A10
68Q40
Difference equations
Differential Equations
Mathematical analysis
Monoids
68Q40
39A10
13P25
12H10
14Q20
03D35
Online AccessGet full text

Cover

More Information
Summary:We study solutions of difference equations in the rings of sequences and, more generally, solutions of equations with a monoid action in the ring of sequences indexed by the monoid. This framework includes, for example, difference equations on grids (for example, standard difference schemes) and difference equations in functions on words. On the universality side, we prove a version of strong Nullstellensatz for such difference equations under the assumption that the cardinality of the ground field is greater than the cardinality of the monoid and construct an example showing that this assumption cannot be omitted. On the undecidability side, we show that the following problems are undecidable:
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2020.14