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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 1, Pages 17–60 (Mi izv623)  

This article is cited in 3 scientific papers (total in 3 papers)

Regular Mittag-Leffler kernels and spectral decomposition of a class of non-selfadjoint operators

G. M. Gubreev

South Ukrainian State K. D. Ushynsky Pedagogical University

Abstract: We define abstract Mittag-Leffler kernels with values in a separable Hilbert space. A Mittag-Leffler kernel is said to be $c$-regular (resp. $d$-regular) if it generates an integral transform of Fourier–Dzhrbashyan type (resp. if the space has an unconditional basis consisting of values of the kernel). We give a complete description of $d$-regular and $c$-regular kernels, which enables us to answer a question of M. G. Krein. We apply the notion of a regular Mittag-Leffler kernel to construct the spectral decomposition for one-dimensional perturbations of fractional powers of dissipative Volterra operators.

DOI: https://doi.org/10.4213/im623

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English version:
Izvestiya: Mathematics, 2005, 69:1, 15–57

Bibliographic databases:

UDC: 517.43+513.88
MSC: 47A45, 47B32, 30D15, 46B15, 42A50
Received: 05.08.2003

Citation: G. M. Gubreev, “Regular Mittag-Leffler kernels and spectral decomposition of a class of non-selfadjoint operators”, Izv. RAN. Ser. Mat., 69:1 (2005), 17–60; Izv. Math., 69:1 (2005), 15–57

Citation in format AMSBIB
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  • https://doi.org/10.4213/im623
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kochubei A.N., “Asymptotic Properties of Solutions of the Fractional Diffusion-Wave Equation”, Fract. Calc. Appl. Anal., 17:3 (2014), 881–896  crossref  mathscinet  zmath  isi  scopus
    2. G. M. Gubreev, V. N. Levchuk, “Description of Unconditional Bases Formed by Values of the Dunkl Kernels”, Funct. Anal. Appl., 49:1 (2015), 64–66  mathnet  crossref  crossref  zmath  isi  elib
    3. Gubreev G. Tarasenko A., “On the Theory of Unconditional Bases of Hilbert Spaces Formed By Entire Vector-Functions”, Bol. Soc. Mat. Mex., 24:1 (2018), 269–278  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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