M. V. Markin

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Articles: 5

On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators

Marat V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 22 (2016), no. 2, 169-183

A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable $C_0$-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.

On the Carleman ultradifferentiable vectors of a scalar type spectral operator

Marat V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 21 (2015), no. 4, 361-369

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.

A note on one decomposition of Banach spaces

M. V. Markin

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 12 (2006), no. 3, 254-257

For a scalar type spectral operator $A$ in complex Banach space $X$, the decomposition of $X$ into the direct sum \begin{equation*} X=\ker A\oplus \overline{R(A)}, \end{equation*} where $\ker A$ is the kernel of $A$ and $\overline{R(A)}$ is the closure of its range $R(A)$ is established.

A Gelfand-Mazur type theorem for normed algebras

Marat V. Markin

Methods Funct. Anal. Topology 11 (2005), no. 1, 63-64

On a characterization of the generators of analytic semigroups in the cass of normal operators

M. V. Markin

Methods Funct. Anal. Topology 2 (1996), no. 2, 86-93


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