dynamic operator
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2020 ◽  
Vol 97 ◽  
pp. 102007 ◽  
Author(s):  
Gabriel Bugár ◽  
Marcel Vološin ◽  
Taras Maksymyuk ◽  
Jana Zausinová ◽  
Vladimír Gazda ◽  
...  


2019 ◽  
Vol 27 (4) ◽  
pp. 469-486
Author(s):  
Siamak RabieniaHaratbar

Abstract Let X be an open subset of {\mathbb{R}^{2}} . We study the dynamic operator, {\mathcal{A}} , integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be recovered by the data-set. Our results show that not all singularities can be recovered as the object moves with a speed lower than the X-ray source. We establish stability estimates and prove that the injectivity and stability are of a generic set if the dynamic operator satisfies the visibility, no conjugate points, and local Bolker conditions. We also show this results can be implemented to fan beam geometry.



Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3843-3851
Author(s):  
Hüseyin Tuna ◽  
Songül Bayrak

In this work, we consider a singular fourth order dynamic operator on time scales. We construct a space of boundary values. Later, we give a description of all maximal dissipative, self-adjoint and other extensions of singular fourth order differential operators on unbounded time scales.





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