Differential Operator Realization of the Exceptional Superalgebra D (2,1;α) and Its Application

2012 ◽  
Vol 57 (5) ◽  
pp. 825-832 ◽  
Author(s):  
Xi Chen ◽  
Xiang-Mao Ding ◽  
Xiao-Hui Wang ◽  
Wen-Li Yang
Keyword(s):  
Differential Operator ◽  
Operator Realization

scholarly journals Uq(sl(n)) DIFFERENCE OPERATOR REALIZATION

1994 ◽  
Vol 09 (35) ◽  
pp. 3273-3283 ◽  
Author(s):  
AZIZOLLAH SHAFIEKHANI
Keyword(s):  
Differential Operator ◽  
Irreducible Representation ◽  
Difference Operator ◽  
Systematic Scheme ◽  
Operator Realization

A unified and systematic scheme for construction of differential operator realization of any irreducible representation of sl (n) is developed. The q-analog of this unified scheme is used to construct q-difference operator realization of any irreducible representation of Uq(sl(n)). Explicit results for U q( sl (2)), U q( sl (3)) and U q( sl (n)) are given.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

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