Structure theorems for a pair of unbounded selfadjoint operators satisfying a quadratic relation

1992 ◽  
pp. 131-150
Author(s):  
V. Ostrovskii ◽  
Yu. Samoilenko
Keyword(s):  
Quadratic Relation ◽  
Selfadjoint Operators ◽  
Structure Theorems

scholarly journals Families of abelian surfaces with real multiplication over Hilbert modular surfaces

1982 ◽  
Vol 88 ◽  
pp. 17-53 ◽  
Author(s):  
G. van der Geer ◽  
K. Ueno
Keyword(s):  
Endomorphism Ring ◽  
Symplectic Group ◽  
Abelian Surface ◽  
Quadratic Relation ◽  
Holomorphic Map ◽  
Real Multiplication ◽  
Compact Complex Surfaces ◽  
Hilbert Modular Surfaces ◽  
Hilbert Modular ◽  
Abelian Functions

Around the beginning of this century G. Humbert ([9]) made a detailed study of the properties of compact complex surfaces which can be parametrized by singular abelian functions. A surface parametrized by singular abelian functions is the image under a holomorphic map of a singular abelian surface (i.e. an abelian surface whose endomorphism ring is larger than the ring of rational integers). Humbert showed that the periods of a singular abelian surface satisfy a quadratic relation with integral coefficients and he constructed an invariant D of such a relation with respect to the action of the integral symplectic group on the periods.

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.

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 A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials

2018 ◽  
Vol 07 (04) ◽  
pp. 1840002 ◽  
Author(s):  
Chuan-Tsung Chan ◽  
Hsiao-Fan Liu
Keyword(s):  
Orthogonal Polynomials ◽  
Deformation Theory ◽  
Toda Lattice ◽  
Quadratic Relation ◽  
Lax Equation ◽  
Toda Equations

Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a [Formula: see text]-deformed version of the Toda equations for both [Formula: see text]-Laguerre/Hermite ensembles, and check the compatibility with the quadratic relation.

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