scholarly journals A HOLOMORPHIC REPRESENTATION OF THE JACOBI ALGEBRA

2006 ◽  
Vol 18 (02) ◽  
pp. 163-199 ◽  
Author(s):  
STEFAN BERCEANU
Keyword(s):  
Hilbert Space ◽  
Differential Operators ◽  
Holomorphic Functions ◽  
First Order ◽  
Polynomial Coefficients ◽  
Holomorphic Representation

A representation of the Jacobi algebra 𝔥1 ⋊ 𝔰𝔲(1, 1) by first-order differential operators with polynomial coefficients on the manifold [Formula: see text] is presented. The Hilbert space of holomorphic functions on which the holomorphic first-order differential operators with polynomials coefficients act is constructed.

scholarly journals Spectrums of Solvable Pantograph Differential-Operators for First Order

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Z. I. Ismailov ◽  
P. Ipek
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Operator Theory ◽  
Differential Operators ◽  
Finite Interval ◽  
Exact Formula ◽  
Operator Expression ◽  
Minimal Operator ◽  
First Order ◽  
Delay Differential

By using the methods of operator theory, all solvable extensions of minimal operator generated by first order pantograph-type delay differential-operator expression in the Hilbert space of vector-functions on finite interval have been considered. As a result, the exact formula for the spectrums of these extensions is presented. Applications of obtained results to the concrete models are illustrated.

scholarly journals On Certain Proximities and Preorderings on the Transposition Hypergroups of Linear First-Order Partial Differential Operators

2014 ◽  
Vol 22 (1) ◽  
pp. 85-103 ◽  
Author(s):  
Jan Chvalina ◽  
Šárka Hošková-Mayerová
Keyword(s):  
Differential Operators ◽  
Partial Differential ◽  
First Order ◽  
Ordered Groups ◽  
Partial Differential Operators ◽  
Power Set

AbstractThe contribution aims to create hypergroups of linear first-order partial differential operators with proximities, one of which creates a tolerance semigroup on the power set of the mentioned differential operators. Constructions of investigated hypergroups are based on the so called “Ends-Lemma” applied on ordered groups of differnetial operators. Moreover, there is also obtained a regularly preordered transpositions hypergroup of considered partial differntial operators.

scholarly journals Root Asymptotics for the Eigenfunctions of Univariate Differential Operators

10.14311/1275 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
B. Shapiro
Keyword(s):  
Differential Operators ◽  
Polynomial Coefficients

This paper is a brief survey of the research conducted by the author and his collaborators in the field of root asymptotics of (mostly polynomial) eigenfunctions of linear univariate differential operators with polynomial coefficients.

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