References
- N. Ahmad, S.K. Sharma and S.A. Mohiuddine, Generalized entire sequence spaces defined by fractional difference operator and sequence of modulus functions, TWMS J. App. and Eng. Math. 10 (2020), 63-72.
- L. Brickman and P.A. Fillmore, The invariant subspace lattice of a linear transformation, Can. J. Math. 19 (1967), 810-822. https://doi.org/10.4153/CJM-1967-075-4
- M.S. Brodskii, Triangular and Jordan Representations of Linear Operators, Translational Mathematical Monographs, 32, AMS Providence, RI, 1971.
- I.H. Dimovski, Convolutional Calculus, Kluwer Academic Publisher, London, 1990.
- I.Y. Domanov and M.M. Malamud, Invariant and hyperinvariant subspaces of an operator Jαand related operator algebras in Sobolev spaces, Linear Algebra and its Appl. 348 (2002), 209-230. https://doi.org/10.1016/S0024-3795(01)00581-X
- N. Dunford and L. Schwartz, Linear Operators, P.I: General Theory, Springer-Verlag, New York, 1958.
- I.C. Gohberg and M.G. Krein, Theory and Applications of Volterra Operators in Hilbert Space, Translational Mathematical Monographs 24, AMS Providence, RI, 1970.
- I.C. Gohberg, P. Lancaster and L. Rodman, Invariant Subspaces of Matrices with Applications, Wiley-Interscience, New York, 1986.
- M. Gurdal, Description of extended eigenvalues and extended eigenvectors of integration operator on the Wiener algebra, Expo. Math. 27 (2009), 153-160. https://doi.org/10.1016/j.exmath.2008.10.006
- M. Gurdal, On the extended eigenvalues and extended eigenvectors of shift operator on the Wiener algebra, Appl. Math. Lett. 22 (2009), 1727-1729. https://doi.org/10.1016/j.aml.2009.06.008
- M. Gurdal, M.T. Garayev and S. Saltan, Some concrete operators and their properties, Turkish J. Math. 39 (2015), 970-989. https://doi.org/10.3906/mat-1502-48
- B.B. Jena, S.K. Paikray, S.A. Mohiuddine and V.N. Mishra, Relatively equi-statistical convergence via deferred Norlund mean based on difference operator of fractional-order and related approximation theorems, AIMS Mathematics 5 (2020), 650-672. https://doi.org/10.3934/math.2020044
- M.T. Karaev, Usage of convolution for the proof of unicellularity, Zap.Nauchn.Sem. LOMI 135 (1984), 66-68.
- M.T. Karaev, Invariant subspaces, cyclic vectors, commutant and extended eigenvectors of some convolution operators, Methods Funct. Anal. Topology 11 (2005), 45-59.
- M.T. Karaev and M. Gurdal, Strongly splitting weighted shift operators on Banach spaces and unicellularity, Oper. Matrices 5 (2011), 157-171.
- M.T. Karaev, M. Gurdal and S. Saltan, Some applications of Banach algebra techniques, Math. Nachr. 284 (2011), 1678-1689. https://doi.org/10.1002/mana.200910129
- M.M. Malamud, Invariant and hyperinvariant subspaces of direct sums of simple Volterra operators, Oper. Theory: Adv. Appl. Integral Differential Oper. 102 (1988), 143-167.
- S.A. Mohiuddine, K. Raj, M. Mursaleen and A. Alotaibi, Linear isomorphic spaces of fractional-order difference operators, Alexandria Eng. J. 60 (2021), 1155-1164. https://doi.org/10.1016/j.aej.2020.10.039
- N.K. Nikolskii, Invariant subspaces in operator theory and function theory, Itogi Nauki i Tekniki, Ser. Mat. Analiz, Moscow, 12 (1974), 199-412.
- N.K. Nikolskii, Treatise on the Shift Operator, Springer, Berlin, 1986.
- P.V. Ostapenko and V.G. Tarasov, Unicellularity of the integration operator in certain function spaces, Teor. Funkcii, Funkcional Anal. i Prilojen 27 (1977), 121-128.
- S. Saltan and M. Gurdal, Spectral multiplicities of some operators, Complex Var. Elliptic Equ. 56 (2011), 513-520. https://doi.org/10.1080/17476933.2010.487207
- R. Tapdigoglu, Invariant subspaces of Volterra integration operator: Axiomatical approach, Bull. Sci. Math. 136 (2012), 574-578. https://doi.org/10.1016/j.bulsci.2011.12.006
- R. Tapdigoglu, On the description of invariant subspaces in the space C(n)[0, 1], Houston J. Math. 39 (2013), 169-176.
- E.R. Tsekanovskii, About description of invariant subspaces and unicellularity of the integration operator in the space W2(p), Uspehi Mat. Nauk. 6 (1965), 169-172.
- N.M. Wigley, The Duhamel product of analytic functions, Duke Math. J. 41 (1974), 211-217. https://doi.org/10.1215/S0012-7094-74-04123-4
- T. Yaying, B. Hazarika and S.A. Mohiuddine, On difference sequence spaces of fractional order involving Padovan numbers, Asian-European J. Math. 14 (2020), doi: 10.1142/S1793557121500959.