Minimaxity and Equivariance in Infinite Dimension

1999 ◽  
Vol 43 (3) ◽  
pp. 388-404
Author(s):  
H. Luschgy
Keyword(s):  
Infinite Dimension

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
Polycyclic Groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

scholarly journals Sharp tunneling estimates for a double-well model in infinite dimension

2021 ◽  
Vol 281 (3) ◽  
pp. 109029
Author(s):  
Morris Brooks ◽  
Giacomo Di Gesù
Keyword(s):  
Infinite Dimension ◽  
Well Model

Pseudoprojective strongly minimal sets are locally projective

1991 ◽  
Vol 56 (4) ◽  
pp. 1184-1194 ◽  
Author(s):  
Steven Buechler
Keyword(s):  
Predicate Symbol ◽  
Infinite Dimension ◽  
Elementary Extension ◽  
Morley Rank ◽  
Minimal Set ◽  
Unary Predicate ◽  
Minimal Sets

AbstractLet D be a strongly minimal set in the language L, and D′ ⊃ D an elementary extension with infinite dimension over D. Add to L a unary predicate symbol D and let T′ be the theory of the structure (D′, D), where D interprets the predicate D. It is known that T′ is ω-stable. We proveTheorem A. If D is not locally modular, then T′ has Morley rank ω.We say that a strongly minimal set D is pseudoprojective if it is nontrivial and there is a k < ω such that, for all a, b ∈ D and closed X ⊂ D, a ∈ cl(Xb) ⇒ there is a Y ⊂ X with a ∈ cl(Yb) and ∣Y∣ ≤ k. Using Theorem A, we proveTheorem B. If a strongly minimal set D is pseudoprojective, then D is locally projective.The following result of Hrushovski's (proved in §4) plays a part in the proof of Theorem B.Theorem C. Suppose that D is strongly minimal, and there is some proper elementary extension D1 of D such that the theory of the pair (D1, D) is ω1-categorical. Then D is locally modular.

scholarly journals Examples of S—expansions of Lie Algebras

2021 ◽  
Vol 2090 (1) ◽  
pp. 012067
Author(s):  
G. Javier Rosales
Keyword(s):  
Lie Algebras ◽  
Three Dimensional ◽  
Infinite Dimension ◽  
Dimensional Case ◽  
Finite Dimensional ◽  
Finite Dimensional Case

Abstract In this note, we give examples of S—expansions of Lie algebras of finite and infinite dimension. For the finite dimensional case, we expand all real three-dimensional Lie algebras. In the case of infinite dimension, we perform contractions obtaining new Lie algebras of infinite dimension.

scholarly journals On stabilization of partial differential equations by noise

2001 ◽  
Vol 161 ◽  
pp. 155-170 ◽  
Author(s):  
Tomás Caraballo ◽  
Kai Liu ◽  
Xuerong Mao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Partial Differential Equations ◽  
Finite Dimension ◽  
Infinite Dimension ◽  
Stability Criteria ◽  
Partial Differential ◽  
Almost Sure Exponential Stability

Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, some stability criteria from Chow [4] and Haussmann [6] are improved and subsequently applied to certain situations, on which the original criteria commonly do not work, to ensure almost sure exponential stability. This paper also extends to infinite dimension some results due to Mao [9] on stabilization of differential equations in finite dimension.

A Purity Criterion for Pairs of Linear Transformations

1974 ◽  
Vol 26 (3) ◽  
pp. 734-745 ◽  
Author(s):  
Uri Fixman ◽  
Frank A. Zorzitto
Keyword(s):  
Perturbation Methods ◽  
Eigenvalue Problems ◽  
Vector Spaces ◽  
Infinite Dimension ◽  
Linear Transformations ◽  
Complex Vector ◽  
Algebraic Investigation ◽  
Image Position

In connection with the study of perturbation methods for differential eigenvalue problems, Aronszajn put forth a theory of systems (X, Y; A, B) consisting of a pair of linear transformations A, B:X → Y (see [1]; cf. also [2]). Here X and Y are complex vector spaces, possibly of infinite dimension. The algebraic aspects of this theory, where no restrictions of topological nature are imposed, where developed in [3] and [5]. We hasten to point out that the category of C2-systems (definition in § 1) in which this algebraic investigation takes place is equivalent to the category of all right modules over the ring of matrices of the form

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