boundary uniqueness
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2014 ◽  
Vol 60 (7) ◽  
pp. 945-950 ◽  
Author(s):  
Abtin Daghighi ◽  
Steven G. Krantz
Keyword(s):  

2014 ◽  
Vol 22 (2) ◽  
pp. 109-120
Author(s):  
Özkan Karaman

AbstractIn this paper, using the boundary properties of the analytic functions we investigate the structure of the discrete spectrum of the boundary value problem (0.1)$$\matrix{\hfill {iy_1^\prime + q_1 \left(x \right)y_2 - \lambda y_1 = \varphi _1 \left(x \right)\;\;} & \hfill {} \cr \hfill {- iy_2^\prime + q_2 \left(x \right)y_1 - \lambda y_2 = \varphi _2 \left(x \right),} & \hfill {x \in R_ + } \cr }$$ and the condition (0.2)$$\left({a_1 \lambda + b_1 } \right)y_2 \left({0,\lambda } \right) - \left({a_2 \lambda + b_2 } \right)y_1 \left({0,\lambda } \right) = 0$$ where q1,q2, φ1, φ2 are complex valued functions, ak ≠ 0, bk ≠ 0, k = 1, 2 are complex constants and λ is a spectral parameter. In this article, we investigate the spectral singularities and eigenvalues of (0.1), (0.2) using the boundary uniqueness theorems of analytic functions. In particular, we prove that the boundary value problem (0.1), (0.2) has a finite number of spectral singularities and eigenvalues with finite multiplicities under the conditions, $$\matrix{{\mathop {\sup }\limits_{x \in R_ + } \left[ {\left| {\varphi _k \left(x \right)} \right|\exp \left({\varepsilon x^\delta } \right)} \right] < \infty ,\;\;\;k = 1.2} \hfill \cr {\mathop {\sup }\limits_{x \in R_ + } \left[ {\left| {q_k \left(x \right)} \right|\exp \left({\varepsilon x^\delta } \right)} \right] < \infty ,\;\;\;k = 1.2} \hfill \cr }$$ for some ε > 0, ${1 \over 2} < \delta < 1$


2006 ◽  
Vol 61 (6) ◽  
pp. 1170-1172 ◽  
Author(s):  
M Deza ◽  
Mikhail I Shtogrin
Keyword(s):  

2006 ◽  
Vol 253 (1) ◽  
pp. 115-122
Author(s):  
V. V. Napalkov ◽  
K. V. Trunov ◽  
R. S. Yulmukhametov

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