Corpus ID: 116362428

SUMMATION OF TWO OPERATOR SERIES CONTAINING THE LAPLACE OPERATOR

@inproceedings{Karachik2007SUMMATIONOT,
  title={SUMMATION OF TWO OPERATOR SERIES CONTAINING THE LAPLACE OPERATOR},
  author={V. Karachik},
  year={2007}
}
System of functions which is f -normalized with respect to 1 ( ) L I , (I is the identical operator) is called f -normalized with respect to 1. L In this case 1 0( ) ( ); L f x f x = 1 1 ( ) ( ) . k k L f x f x k N − = , ∈ The main property of the system of functions { } ( ) : 0 1 2, ... k f x k = , , f -normalized with respect to operators 1 2 ( ) L L , in the domain Ω is in the following: the series 

References

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Normalized system of functions with respect to the Laplace operator and its applications
A review of the decomposition method in applied mathematics