Structure Theorems for $$\mathcal H(A, B)$$ Spaces

2020 ◽  
pp. 53-68
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Irene Sabadini
Keyword(s):  
Structure Theorems

scholarly journals Convolutors on $${\mathcal S}_{\omega }({\mathbb R}^N)$$

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Angela A. Albanese ◽  
Claudio Mele
Keyword(s):  
Fourier Transform ◽  
Dual Space ◽  
Strong Operator ◽  
Dual Spaces ◽  
Structure Theorems ◽  
The Fourier Transform ◽  
Decreasing Functions

AbstractIn this paper we continue the study of the spaces $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) and $${\mathcal O}_{C,\omega }({\mathbb R}^N)$$ O C , ω ( R N ) undertaken in Albanese and Mele (J Pseudo-Differ Oper Appl, 2021). We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) is the space of convolutors of the space $${\mathcal S}_\omega ({\mathbb R}^N)$$ S ω ( R N ) of the $$\omega $$ ω -ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $${\mathcal S}'_\omega ({\mathbb R}^N)$$ S ω ′ ( R N ) . We also establish that the Fourier transform is an isomorphism from $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) onto $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) . In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $${\mathcal L}_b({\mathcal S}_\omega ({\mathbb R}^N))$$ L b ( S ω ( R N ) ) and the last space is endowed with its natural lc-topology.

scholarly journals Structure theorems in tame expansions of o-minimal structures by a dense set

2020 ◽  
Vol 239 (1) ◽  
pp. 435-500 ◽  
Author(s):  
Pantelis E. Eleftheriou ◽  
Ayhan Günaydin ◽  
Philipp Hieronymi
Keyword(s):  
Structure Theorems ◽  
Dense Set

On feckly polar rings

2019 ◽  
Vol 18 (02) ◽  
pp. 1950021
Author(s):  
Tugce Pekacar Calci ◽  
Huanyin Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Structure Theorems ◽  
Regular Rings

In this paper, we introduce a new notion which lies properly between strong [Formula: see text]-regularity and pseudopolarity. A ring [Formula: see text] is feckly polar if for any [Formula: see text] there exists [Formula: see text] such that [Formula: see text] Many structure theorems are proved. Further, we investigate feck polarity for triangular matrix and matrix rings. The relations among strongly [Formula: see text]-regular rings, pseudopolar rings and feckly polar rings are also obtained.

Structure theorems for weakly B-abundant semigroups

2011 ◽  
Vol 84 (1) ◽  
pp. 39-58 ◽  
Author(s):  
Yanhui Wang
Keyword(s):  
Abundant Semigroups ◽  
Structure Theorems

scholarly journals Structure theorems for game trees

2002 ◽  
Vol 99 (13) ◽  
pp. 9077-9080 ◽  
Author(s):  
S. Govindan ◽  
R. Wilson
Keyword(s):  
Game Trees ◽  
Structure Theorems

scholarly journals Lower Bounds for the Average Genus of a CF-graph

10.37236/422 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Yichao Chen
Keyword(s):  
Lower Bound ◽  
Linear Function ◽  
Lower Bounds ◽  
Betti Number ◽  
Maximum Genus ◽  
Simple Graphs ◽  
Structure Theorems ◽  
Average Genus

CF-graphs form a class of multigraphs that contains all simple graphs. We prove a lower bound for the average genus of a CF-graph which is a linear function of its Betti number. A lower bound for average genus in terms of the maximum genus and some structure theorems for graphs with a given average genus are also provided.

scholarly journals Asymptotic expansion in measure and strong ergodicity

2021 ◽  
pp. 1-39
Author(s):  
Kang Li ◽  
Federico Vigolo ◽  
Jiawen Zhang
Keyword(s):  
Asymptotic Expansion ◽  
Recent Result ◽  
Spectral Gaps ◽  
Strong Ergodicity ◽  
Classical Notion ◽  
Structure Theorems ◽  
New Perspective

In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalizes expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure theorems for asymptotically expanding actions, showing that they admit exhaustions by domains of expansion. As an application, we recover a recent result of Marrakchi, characterizing strong ergodicity in terms of local spectral gaps. We also show that homogeneous strongly ergodic actions are always expanding in measure and establish a connection between asymptotic expansion in measure and asymptotic expanders by means of approximating spaces.

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