Results 11 to 20 of about 109 (35)
On an abstract evolution equation with a spectral operator of scalar type [PDF]
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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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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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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Isomorphisms of $BV(\sigma)$ spaces
, 2021 In this paper we investigate the relationship between the properties of a compact set $\sigma \subseteq \mathbb{C}$ and the structure of the space $BV(\sigma)$ of functions of bounded variation (in the sense of Ashton and Doust) defined on $\sigma$.
Al-shakarchi, Shaymaa, Doust, Ian
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Cohyponormal operators with the single valued extension property
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 4, Page 659-663, 1986., 1986 It is proved that in order to find a nontrivial hyperinvariant subspace for a cohyponormal operator it suffices to make the further assumption that the operator have the single‐valued extension property.
Ridgley Lange, Shengwang Wang
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 In this paper, using the boundary properties of the analytic functions we investigate the structure of the discrete spectrum of the boundary value problem (0.1)iy1'+q1(x)y2−λy1=ϕ1(x) −iy2'+q2(x)y1−λy2=ϕ2(x),x∈R+$$\matrix{\hfill {iy_1^\prime + q_1 \left ...
Karaman Özkan
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Paley-Littlewood decomposition for sectorial operators and interpolation spaces [PDF]
, 2016 We prove Paley-Littlewood decompositions for the scales of fractional powers of $0$-sectorial operators $A$ on a Banach space which correspond to Triebel-Lizorkin spaces and the scale of Besov spaces if $A$ is the classical Laplace operator on $L^p ...
Kriegler, Christoph, Weis, Lutz
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The Kluvanek‐Kantorovitz characterization of scalar operators in locally convex spaces
International Journal of Mathematics and Mathematical Sciences, Volume 5, Issue 2, Page 345-349, 1982., 1982 This paper is devoted to a proof of the characterization without duality theory, using strong integrals, while eliminating any assumptions of barrelledness or equicontinuity.
William V. Smith
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