polynomial operator
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2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Michael Gil’

We consider the equations∑k=0mcm-kAkXBk=Cand∑k=0mcm-kAkXBm-k=C, whereck∈C  (k=1,…,m),c0=1,A,B,Care given linear bounded operators in a Banach space andXis to be found. Representations of solutions are derived. In the cases of Euclidean and Hilbert spaces, norm estimates for the solutions are suggested.


2013 ◽  
Vol 143 (6) ◽  
pp. 1147-1162 ◽  
Author(s):  
Qing-Ming Cheng ◽  
He-Jun Sun ◽  
Guoxin Wei ◽  
Lingzhong Zeng

In this paper, we investigate the Dirichlet eigenvalue problems of the poly-Laplacian with any order and the quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first k eigenvalues.


2013 ◽  
Vol 22 (8) ◽  
pp. 080301 ◽  
Author(s):  
Hong-Yi Fan ◽  
Rui He ◽  
Cheng Da ◽  
Zu-Feng Liang

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