scholarly journals The Null Space Pursuit Algorithm based on an Arbitrary Even-Order Differential Operator

2015 ◽  
Author(s):  
W. W. Xiao ◽  
Y. X. Guo
Keyword(s):  
Differential Operator ◽  
Null Space ◽  
Order Differential Operator ◽  
Even Order

Krein Extension of an Even-Order Differential Operator

2018 ◽  
Vol 54 (4) ◽  
pp. 551-556
Author(s):  
Ya. I. Granovskyi ◽  
L. L. Oridoroga
Keyword(s):  
Differential Operator ◽  
Order Differential Operator ◽  
Even Order ◽  
Krein Extension

scholarly journals On the Sampson Laplacian

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1059-1070 ◽  
Author(s):  
Sergey Stepanov ◽  
Irina Tsyganok ◽  
Josef Mikes
Keyword(s):  
Differential Operator ◽  
Laplace Operator ◽  
Riemannian Manifolds ◽  
Analytical Method ◽  
Null Space ◽  
Second Order ◽  
Order Differential Operator ◽  
Vanishing Theorems ◽  
Symmetric Tensors ◽  
Lowest Eigenvalue

In the present paper we consider the little-known Sampson operator that is strongly elliptic and self-adjoint second order differential operator acting on covariant symmetric tensors on Riemannian manifolds. First of all, we review the results on this operator. Then we consider the properties of the Sampson operator acting on one-forms and symmetric two-tensors. We study this operator using the analytical method, due to Bochner, of proving vanishing theorems for the null space of a Laplace operator admitting a Weitzenb?ck decomposition. Further we estimate operator?s lowest eigenvalue.

A nonlocal problem for a differential operator of even order with involution

2020 ◽  
Vol 26 (2) ◽  
pp. 297-307
Author(s):  
Petro I. Kalenyuk ◽  
Yaroslav O. Baranetskij ◽  
Lubov I. Kolyasa
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riesz Basis ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Nonlocal Problem ◽  
Even Order

AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

scholarly journals Gap opening in two-dimensional periodic systems

2019 ◽  
Vol 23 (01) ◽  
pp. 1950080
Author(s):  
D. I. Borisov ◽  
P. Exner
Keyword(s):  
Differential Operator ◽  
Finite Number ◽  
Distinctive Feature ◽  
Perturbation Parameter ◽  
Periodic Systems ◽  
Order Differential Operator ◽  
Two Dimensional ◽  
Gap Opening ◽  
Gap Control ◽  
Waveguide System

We present a new method of gap control in two-dimensional periodic systems with the perturbation consisting of a second-order differential operator and a family of narrow potential “walls” separating the period cells in one direction. We show that under appropriate assumptions one can open gaps around points determined by dispersion curves of the associated “waveguide” system, in general any finite number of them, and to control their widths in terms of the perturbation parameter. Moreover, a distinctive feature of those gaps is that their edge values are attained by the corresponding band functions at internal points of the Brillouin zone.

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