4 citations · 27 across the 22 of their papers we have counts for
25 papers
On hypercyclicity and linear chaos in a nonclassical sequence space and beyond
Marat V. Markin, Eric Montoya
We analyze the hypercyclicity, chaoticity, and spectral structure of (bounded and unbounded) weighted backward shifts in a nonclassical sequence space, which the space of sum…
On linear chaos in the spaces of vanishing and convergent sequences
Marat V. Markin, Gabriel Martinez Lazaro, Edward S. Sichel
We study the chaoticity of bounded and unbounded weighted backward shifts in the space of vanishing sequences via a novel straightforward approach based on a newl…
On asymptotics for -semigroups
Marat V. Markin
We stretch the spectral bound equal growth bound condition along with a generalized Lyapunov stability theorem, known to hold for -semigroups of normal operators on complex Hi…
An observation on unbounded linear operators with an arbitrary spectrum
Marat V. Markin
We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset…
On sufficient and necessary conditions for linear hypercyclicity and chaos
Marat V. Markin
By strengthening one of the hypotheses of a well-known sufficient condition for the hypercyclicity of linear operators in Banach spaces, we arrive at a sufficient condition for lin…
On the chaoticity of derivatives
Marat V. Markin
We utilize a recently established by the author sufficient condition for linear chaos to prove the chaoticity of derivatives in the spaces and ($-\infty<a<b<\in…
On a characterization of convergence in Banach spaces with a Schauder basis
Marat V. Markin, Olivia B. Soghomonian
We extend the well-known characterizations of convergence in the spaces () of -summable sequence and of vanishing sequences to a general characterizat…
On the regularity of scalar type spectral -semigroups
Marat V. Markin
We show that, for the -semigroups of scalar type spectral operators, a well-known necessary condition for the generation of eventually norm-continuous -semigroups, formul…
On a characterization of finite-dimensional vector spaces
Marat V. Markin
We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.
On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups
Marat V. Markin
We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spe…
On linear chaos in function spaces
John M. Jimenez, Marat V. Markin
We show that, in (), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbou…
On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis
Marat V. Markin
Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\in \mathbb{R}, \] with a scalar type spectral operator in a complex Banach space, we find conditions on , formulated…
On expansions
Marat V. Markin, Edward S. Sichel
When finding an original proof to a known result describing expansions on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to to…
On the non-hypercyclicity of normal operators, collections of their exponentials, and symmetric operators
Marat V. Markin, Edward S. Sichel
We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary normal operator (bounded or unbounded) in a complex Hilbert space as well as of the collection…
On general construct of chaotic unbounded linear operators in Banach Spaces with Schauder Bases
Marat V. Markin
We utilize the idea underlying the construct of the classical weighted backward shift Rolewicz's operators to furnish a straightforward approach to a general construct of chaotic u…
On the chaoticity and spectral structure of Rolewicz-type unbounded operators
Marat V. Markin
We prove the chaoticity and describe the spectral structure of Rolewicz-type weighted backward shift unbounded linear operators in the sequence spaces () and $…
On the non-hypercyclicity of scalar type spectral operators and collections of their exponentials
Marat V. Markin
Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a (bounded or unbounded) scalar type spectral op…
On the differentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis
Marat V. Markin
Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\in \mathbb{R}, \] with scalar type spectral operator in a complex Banach space, found are conditions necessary and suff…
On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one
Marat V. Markin
It is shown that, if all weak solutions of the evolution equation \begin{equation*} y'(t)=Ay(t),\ t\ge0, \end{equation*} with a scalar type spectral operator in a complex Banac…
On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator
Marat V. Markin
Found are conditions on a scalar type spectral operator in a complex Banach space necessary and sufficient for all weak solutions of the evolution equation \begin{equation*} y'…
On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis
Marat V. Markin
Given the abstract evolution equation \[ y'(t)=Ay(t),\ t\ge 0, \] with scalar type spectral operator in a complex Banach space, found are conditions necessary and sufficient fo…
On the mean ergodicity of weak solutions of an abstract evolution equation
Marat V. Markin
Found are conditions of rather general nature sufficient for the existence of the limit at infinity of the Cesàro means \begin{equation*} \frac{1}{t} \int_0^ty(s)\,ds \end{equation…
On certain spectral features inherent to scalar type spectral operators
Marat V. Markin
Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral…
On the generation of Beurling type Carleman ultradifferentiable -semigroups by scalar type spectral operators
Marat V. Markin
A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable -semigroups is established, the important case of the Gevrey ultradiffe…