Results 1 to 10 of about 37 (37)
Some new results on the weaving of K-g-frames in Hilbert spaces
Open Mathematics, 2021 In this paper, we provide some conditions for a K-woven pair of K-g-frames to be preserved under an operator and particularly, we report that applying two different operators to a K-woven pair of K-g-frames can leave them K-woven.
Xiang Zhong-Qi
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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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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2401-2422, 2004., 2004 Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
Marat V. Markin
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On the Carleman classes of vectors of a scalar type spectral operator
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 60, Page 3219-3235, 2004., 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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Local spectral theory of endomorphisms of the disk algebra
Demonstratio Mathematica, 2016 Let A(𝔻) denote the disk algebra. Every endomorphism of A(𝔻) is induced by some ϕ ∈ A(𝔻) with ‖ϕ‖ ≤ 1. In this paper, it is shown that if ϕ is not an automorphism of 𝔻 and ϕ has a fixed point in the open unit disk then the endomorphism induced by ϕ is ...
Trivedi Shailesh, Chandra Harish
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Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1007-1018, 2004., 2004 In the class of scalar type spectral operators in a complex Banach space, a characterization of the generators of analytic C0‐semigroups in terms of the analytic vectors of the operators is found.
Marat V. Markin
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A note on the spectral operators of scalar type and semigroups of bounded linear operators
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 635-640, 2002., 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 conditions on the resolvent of the generator being automatically met and the corresponding semigroup ...
Marat V. Markin
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Open Mathematics, 2019 It is shown that, if all weak solutions of the evolution ...
Markin Marat V.
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On an abstract evolution equation with a spectral operator of scalar type
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 9, Page 555-563, 2002., 2002 It is shown that the weak solutions of the evolution equation y′(t) = Ay(t), t ∈ [0, T) (0 < T ≤ ∞), where A is a spectral operator of scalar type in a complex Banach space X, defined by Ball (1977), are given by the formula y(t) = e tAf, t ∈ [0, T), with the exponentials understood in the sense of the operational calculus for such operators and the ...
Marat V. Markin
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