Spectral analysis of biorthogonal expansions generated by Muckenhoupt weights

Gubreev, G. M.

doi:10.1007/bf02111293

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…An interesting problem is whether there is a system of eigenvectors of −RJ 2−α L which creates a Riesz basis of L 2 (0, 1). This problem was investigated in [15,16] who gave conditions under which the system…”

Section: Thusmentioning

confidence: 99%

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On analytic semigroup generators involving Caputo fractional derivative

Grabowski

2022

EECT

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<p style='text-indent:20px;'>Our investigations are motivated by the well - posedness problem of some dynamical models with anomalous diffusion described by the Caputo spatial fractional derivative of order <inline-formula><tex-math id="M1">\begin{document}$ \alpha \in (1, 2) $\end{document}</tex-math></inline-formula>. We propose a characterization of an exponentially stable analytic semigroup generator using the inverse operator. This characterization enables us to establish the form of a generator involving the Caputo fractional derivative, under various boundary conditions. In particular, the results simplify those known from literature obtained by means of the fractional Sobolev spaces and some perturbation results. Going further, we show how to construct a control system in factor form, having such a generator as the state operator.</p>

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Section: Thusmentioning

confidence: 99%

“…Presentation of his result as well as examination of its applicability requires advanced concepts of complex analysis and goes far beyond the scope of the present paper. Therefore it is relegated to a future study, especially as none example has been provided in [15,16].…”

Section: Thusmentioning

confidence: 99%

On analytic semigroup generators involving Caputo fractional derivative

Grabowski

2022

EECT

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“…Following [3] and [4], we now present a construction of regular kernels ranging in each of the spaces L 2 (0, σ), σ > 0. Let a Muckenhoupt A 2 γρ -weight w 2 be given on the contour γ ρ , ρ > 1/2, occurring in Definition 2; i.e.,…”

Section: Definition 4 a Kernel E ρ Is Said To Be Regular If It Is Simentioning

confidence: 99%

Regular Mittag-Leffler kernels and Volterra operators

Gubreev¹

2004

Funct Anal Its Appl

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We give the definition of an abstract Mittag-Leffler kernel E ρ ranging in a separable Hilbert space H. In the simplest case, E ρ (z) can be expressed via the Mittag-Leffler function E ρ (z, µ). The kernel E ρ is said to be c-regular if it generates an integral transform of FourierDzhrbashyan type and d-regular if its range contains an unconditional basis of H. We give a complete description of d-and c-regular kernels, which permits us to answer a question posed by M. Krein. An application to the problem on the similarity of a rank one perturbation of a fractional power of a Volterra operator to a normal operator is considered.

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Gubreev¹,

Olefir²

2002

Journal of Mathematical Sciences

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Spectral analysis of biorthogonal expansions generated by Muckenhoupt weights

Cited by 6 publications

References 3 publications

On analytic semigroup generators involving Caputo fractional derivative

On analytic semigroup generators involving Caputo fractional derivative

Regular Mittag-Leffler kernels and Volterra operators

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