scholarly journals Spectral analysis of discrete dirac equation with generalized eigenparameter in boundary condition

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6039-6054 ◽  
Author(s):  
Turhan Koprubasi ◽  
Ram Mohapatra
Keyword(s):  
Boundary Condition ◽  
Spectral Analysis ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Spectral Properties ◽  
Difference Operators ◽  
Spectral Singularities ◽  
First Order ◽  
Complex Sequences

Let L denote the discrete Dirac operator generated in ?2 (N,C2) by the non-selfadjoint difference operators of first order (an+1y(2)n+1 + bny(2)n + pny(1)n = ?y(1)n, an-1y(1)n-1 + bny(1)n + qny(2)n = ?y(2)n, n ? N, (0.1) with boundary condition Xp k=0 (y(2)1?k + y(1)0 ?k)?k=0, (0.2) where (an), (bn), (pn) and (qn), n ? N are complex sequences, ?i; ?i ? C, i = 0, 1, 2,..., p and ? is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ?? n=1 |n|(|1-an| + |1+bn| + |pn| + |qn|) < ? holds.

scholarly journals Spectral properties of the Klein-Gordons-wave equation with spectral parameter-dependent boundary condition

2004 ◽  
Vol 2004 (27) ◽  
pp. 1437-1445
Author(s):  
Gülen Başcanbaz-Tunca
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Differential Operator ◽  
Finite Number ◽  
Spectral Parameter ◽  
Spectral Properties ◽  
Spectral Singularities ◽  
Klein Gordon ◽  
Parameter Dependent ◽  
Complex Valued

We investigate the spectrum of the differential operatorLλdefined by the Klein-Gordons-wave equationy″+(λ−q(x))2y=0,x∈ℝ+=[0,∞), subject to the spectral parameter-dependent boundary conditiony′(0)−(aλ+b)y(0)=0in the spaceL2(ℝ+), wherea≠±i,bare complex constants,qis a complex-valued function. Discussing the spectrum, we prove thatLλhas a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditionslimx→∞q(x)=0,supx∈R+{exp(ϵx)|q′(x)|}<∞,ϵ>0, hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.

SEPARABILITY OF THE MASSIVE DIRAC EQUATION AND HAWKING RADIATION OF DIRAC PARTICLES IN THE CHARGED AdS–KERR–TAUB–NUT BLACK HOLE

2011 ◽  
Vol 26 (20) ◽  
pp. 1509-1520 ◽  
Author(s):  
PU-JIAN MAO ◽  
LIN-YU JIA ◽  
JI-RONG REN
Keyword(s):  
Black Hole ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Thermal Effect ◽  
Hawking Radiation ◽  
Symmetric Operator ◽  
Scalar Particles ◽  
First Order ◽  
Dirac Particles

We investigate the separability of massive Dirac equation in the charged AdS–Kerr–Taub–NUT black hole. It is shown that the Dirac equation can be separated by variables into purely radial and purely angular parts in this background spacetime. From the separated solutions for massive Dirac equation, a first-order symmetric operator that commutes with the Dirac operator is constructed and expressed in terms of Killing–Yano tensor admitted by the charged AdS–Kerr–Taub–NUT spacetime. Then the Hawking radiation of Dirac particles in the background of charged AdS–Kerr–Taub–NUT black hole is investigated via the Damour–Ruffini–Sannan method. It is shown that quantum thermal effect of the Dirac particles in the charged AdS–Kerr–Taub–NUT black hole has the same character with that of the scalar particles.

scholarly journals On Spectral Properties of Compact Toeplitz Operators on Bergman Space with Logarithmically Decaying Symbol and Applications to Banded Matrices

2021 ◽  
Author(s):  
Mahamet Koïta ◽  
Stanislas Kupin ◽  
Sergey Naboko ◽  
Belco Touré
Keyword(s):  
Spectral Analysis ◽  
Continuous Function ◽  
Bergman Space ◽  
Orthogonal Projection ◽  
Spectral Properties ◽  
Toeplitz Operators ◽  
Closed Subspace ◽  
Jacobi Matrices ◽  
Banded Matrices ◽  
Eigen Values

Abstract Let $L^2({{\mathbb{D}}})$ be the space of measurable square-summable functions on the unit disk. Let $L^2_a({{\mathbb{D}}})$ be the Bergman space, that is, the (closed) subspace of analytic functions in $L^2({{\mathbb{D}}})$. $P_+$ stays for the orthogonal projection going from $L^2({{\mathbb{D}}})$ to $L^2_a({{\mathbb{D}}})$. For a function $\varphi \in L^\infty ({{\mathbb{D}}})$, the Toeplitz operator $T_\varphi : L^2_a({{\mathbb{D}}})\to L^2_a({{\mathbb{D}}})$ is defined as $$\begin{align*} & T_\varphi f=P_+\varphi f, \quad f\in L^2_a({{\mathbb{D}}}). \end{align*}$$The main result of this article are spectral asymptotics for singular (or eigen-) values of compact Toeplitz operators with logarithmically decaying symbols, that is, $$\begin{align*} & \varphi(z)=\varphi_1(e^{i\theta})\, (1+\log(1/(1-r)))^{-\gamma},\quad \gamma&gt;0, \end{align*}$$where $z=re^{i\theta }$ and $\varphi _1$ is a continuous (or piece-wise continuous) function on the unit circle. The result is applied to the spectral analysis of banded (including Jacobi) matrices.

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

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