On a completely non-unitary contraction and associated dissipative difference operator
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Authors
Ekin Uğurlu
- Cankaya University, Faculty of Arts and Science, Department of Mathematics, 06530 Balgat, Ankara, Turkey.
Dumitru Baleanu
- Cankaya University, Faculty of Arts and Science, Department of Mathematics, 06530 Balgat, Ankara, Turkey.
- Institute of Space Sciences, Magurele-Bucharest, Romania.
Abstract
In this paper, we investigate the spectral properties of dissipative
difference operator, dissipative sum operator and contractive
operator. Using Solomyak's method, we construct the characteristic
function of the dissipative difference operator. For this purpose,
we use boundary spaces and functional embeddings. Then we pass to
the characteristic function of the Cayley transform of the
dissipative difference operator which is a completely non-unitary
contraction belonging to the class \(C_{0}\). With the aid of this
characteristic function we achieve to pass to the minimal function
of the contraction and we investigate the complete spectral analysis
of both the contractive and dissipative operators. Embedding the
associated contraction to its natural unitary colligation, we obtain a Carathéodory function. Moreover, self-adjoint dilation of the maximal
dissipative difference operator and its incoming and outgoing
eigenfunctions are constructed. Finally, the truncated CMV matrix is
established which is unitary equivalent to the contractive operator.
Share and Cite
ISRP Style
Ekin Uğurlu, Dumitru Baleanu, On a completely non-unitary contraction and associated dissipative difference operator, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5999--6019
AMA Style
Uğurlu Ekin, Baleanu Dumitru, On a completely non-unitary contraction and associated dissipative difference operator. J. Nonlinear Sci. Appl. (2017); 10(11):5999--6019
Chicago/Turabian Style
Uğurlu, Ekin, Baleanu, Dumitru. "On a completely non-unitary contraction and associated dissipative difference operator." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5999--6019
Keywords
- Difference operator
- completely non-unitary contraction
- dissipative operator
- characteristic function
- CMV matrix
MSC
- 47B361
- 47B44
- 47A48
- 34B20
- 62M15
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