Spectral analysis of a class of second-order non-self-adjoint differential operators

1980 ◽  
Vol 14 (1) ◽  
pp. 11-15 ◽  
Author(s):  
M. G. Gasymov
Keyword(s):  
Spectral Analysis ◽  
Differential Operators ◽  
Second Order

scholarly journals Equiconvergence property for spectral expansions related to perturbations of the operator - u''(-x) with initial data

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1069-1078 ◽  
Author(s):  
Leonid Kritskov ◽  
Abdizhahan Sarsenbi
Keyword(s):  
Spectral Analysis ◽  
Initial Data ◽  
Differential Operators ◽  
Second Order ◽  
Spectral Expansions ◽  
Root Functions ◽  
Operator Form ◽  
Complex Valued

Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution: -u''(-x) and -u''(-x) + q(x)u(x) with the initial data u(-1) = 0, u'(-1) = 0 is obtained. Starting with the spectral analysis of the unperturbed operator, the estimates of the Green?s functions are established and then applied via the contour integrating approach to the spectral expansions. As a corollary, it is proved that the root functions of the perturbed operator form the basis in L2(-1,1) for any complex-valued coefficient q(x) ? L2(-1,1).

scholarly journals AdS superprojectors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
E. I. Buchbinder ◽  
D. Hutchings ◽  
S. M. Kuzenko ◽  
M. Ponds
Keyword(s):  
Shell Model ◽  
Differential Operators ◽  
Second Order ◽  
Projection Operators ◽  
De Sitter ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Higher Spin

Abstract Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

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