MARKIN, MARAThttp://hdl.handle.net/10211.3/1800182018-01-20T00:55:47Z2018-01-20T00:55:47ZComment on "On the Carleman Classes of Vectors of a Scalar Type Spectral Operator"Markin, Marat V.http://hdl.handle.net/10211.3/1989422018-01-05T19:53:52Z2018-01-01T00:00:00ZComment on "On the Carleman Classes of Vectors of a Scalar Type Spectral Operator"
Markin, Marat V.
The results of three papers, in which the author inadvertently overlooks certain deficiencies in the descriptions of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a complex Banach space established in βOn the Carleman Classes of Vectors of a Scalar Type Spectral Operator,β Int. J. Math. Math. Sci. 2004 (2004), no. 60, 3219β3235, are observed to remain true due to more recent findings.
Originally published in International Journal of Mathematics and Mathematical Sciences Volume 2018, Article ID 2135740.
2018-01-01T00:00:00ZOn certain spectral features inherent to scalar type spectral operatorsMarkin, Marat V.http://hdl.handle.net/10211.3/1931782017-06-16T17:08:07Z2017-01-01T00:00:00ZOn certain spectral features inherent to scalar type spectral operators
Markin, Marat V.
Important spectral features such as the emptiness of the residual spec- trum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at 0, known to hold for bounded scalar type spectral operators, are shown to naturally transfer to the unbounded case.
From Methods of Functional Analysis and Topology, Vol. 23 (2017), no. 1, pp. 60-65, available online http://mfat.imath.kiev.ua/article/?id=948.
2017-01-01T00:00:00ZOn the Carleman ultradi erentiable vectors of a scalar type spectral operatorMarkin, Marat V.http://hdl.handle.net/10211.3/1800202016-10-28T20:06:34Z2015-01-01T00:00:00ZOn the Carleman ultradi erentiable vectors of a scalar type spectral operator
Markin, Marat V.
A description of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a reflexive complex Banach space is shown to remain true without the reflexivity requirement. A similar nature description of the entire vectors of exponential type, known for a normal operator in a complex Hilbert space, is generalized to the case of a scalar type spectral operator in a complex Banach space.
From Methods of Functional Analysis and Topology, Vol. 21 (2015), no. 4, pp. 361β369, available online http://mfat.imath.kiev.ua/article/?id=838.
2015-01-01T00:00:00ZOn the generation of Beurling type Carleman ultradi erentiable C0-semigroups by scalar type spectral operatorsMarkin, Marat V.http://hdl.handle.net/10211.3/1800192016-10-28T19:54:20Z2016-01-01T00:00:00ZOn the generation of Beurling type Carleman ultradi erentiable C0-semigroups by scalar type spectral operators
Markin, Marat V.
A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable C0-semigroups is established, the important case of the Gevrey ultradifferentiability is considered in detail, the implementation of the general criterion corresponding to a certain rapidly growing defining sequence is observed.
From Methods Funct. Anal. Topology, Volume 22, Number 2, 2016, pp. 169-183, available online http://mfat.imath.kiev.ua/article/?id=848.
2016-01-01T00:00:00Z