This article is cited in 6 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.

UDC: 517.43+513.88

MSC: 47A45, 47B32, 30D15, 46B15, 42A50

Received: 05.08.2003

DOI: 10.4213/im623

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

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