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This article is cited in 4 scientific papers (total in 4 papers)
Spectral analysis of biorthogonal expansions of functions, and exponential series
G. M. Gubreev
Abstract:
The author studies the spectral properties of the operator $A=i\frac d{dt}$ in the space $L_2(0,1)$, whose domain of definition is the kernel of some functional that is bounded in $W_2^1(0,1)$ but not bounded in $L_2(0,1)$. Necessary and sufficient conditions are given under which the operators $\pm iA$ generate $C_0$-semigroups, and criteria for the similarity of $A$ with a dissipative operator are proved. The results are used to study the basis properties of families of exponentials and to solve S. G. Krein's problem on the description of generators of semigroups in terms of their dissipative extensions. The solvability of integral equations of Delsarte type for mean periodic extensions of functions is also proved.
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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:3, 573–605
Bibliographic databases:
 
UDC:
517.5
MSC: Primary 47E05, 47D05, 34B25; Secondary 30B60, 30D15, 42C30, 46E30
Received: 08.12.1986
Citation:
G. M. Gubreev, “Spectral analysis of biorthogonal expansions of functions, and exponential series”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989), 1236–1268; Math. USSR-Izv., 35:3 (1990), 573–605
Citation in format AMSBIB
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\by G.~M.~Gubreev
\paper Spectral analysis of biorthogonal expansions of functions, and exponential series
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 6
\pages 1236--1268
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1039963}
\zmath{https://zbmath.org/?q=an:0705.42022}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 3
\pages 573--605
\crossref{https://doi.org/10.1070/IM1990v035n03ABEH000718}
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This publication is cited in the following articles:
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G. M. Gubreev, “On a class of unconditional bases in Hilbert spaces and on the problem of similarity of dissipative Volterra operators”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 93–126
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A. M. Minkin, “A first-order boundary value problem with boundary condition on a countable set of points”, Math. Notes, 62:3 (1997), 350–355
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G. M. Gubreev, “$L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials”, Sb. Math., 190:12 (1999), 1715–1747
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G. M. Gubreev, A. A. Tarasenko, “Spectral decomposition of model operators in de Branges spaces”, Sb. Math., 201:11 (2010), 1599–1634
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