On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator on the Real Axis [PDF]
International Journal of Mathematics and Mathematical Sciences, 2018 Given the abstract evolution equation y′(t)=Ay(t), t∈R, with scalar type spectral operator A in a complex Banach space, found are conditions necessary and sufficient for all weak solutions of the equation, which a priori need not be strongly ...
Marat V. Markin
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Comment on “On the Carleman Classes of Vectors of a Scalar Type Spectral Operator” [PDF]
International Journal of Mathematics and Mathematical Sciences, 2018 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 ...
Marat V. Markin
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On the Carleman classes of vectors of a scalar type spectral operator [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator's resolution of the identity. A theorem of the Paley-Wiener type is considered as an application.
Marat V. Markin
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When is a non-self-adjoint Hill operator a spectral operator of scalar type? [PDF]
Comptes Rendus. Mathématique, 2005 We derive necessary and sufficient conditions for a one-dimensional periodic Schr\"odinger (i.e., Hill) operator H=-d^2/dx^2+V in L^2(R) to be a spectral operator of scalar type.
Gesztesy, Fritz, Tkachenko, Vadim
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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis [PDF]
Open Mathematics, 2020 Given the abstract evolution equation y′(t)=Ay(t),t∈ℝ,y^{\prime} (t)=Ay(t),t\in {\mathbb{R}}, with a scalar type spectral operator A in a complex Banach space, we find conditions on A, formulated exclusively in terms of the location of its spectrum in ...
Markin Marat V.
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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis [PDF]
Open Mathematics, 2019 Given the abstract evolution ...
Markin Marat V.
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On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one [PDF]
Open Mathematics, 2019 It is shown that, if all weak solutions of the evolution ...
Markin Marat V.
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On the Differentiability of Weak Solutions of an Abstract Evolution Equation with a Scalar Type Spectral Operator [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 For the evolution equation 𝑦(𝑡)=𝐴𝑦(𝑡) with a scalar type spectral operator 𝐴 in a Banach space, conditions on 𝐴 are found that are necessary and sufficient for all weak solutions of the equation on [0,∞) to be strongly infinite differentiable on [0 ...
Marat V. Markin
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On an abstract evolution equation with a spectral operator of scalar type
International Journal of Mathematics and Mathematical Sciences, 2002 It is shown that the weak solutions of the evolution equation y′(t)=Ay(t), t∈[0,T ...
Marat V. Markin
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A note on the spectral operators of scalar type and semigroups of bounded linear operators [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0- and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the ...
Marat V. Markin
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