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Izvestiya: Mathematics, 2009, Volume 73, Issue 2, Pages 215–278
DOI: https://doi.org/10.1070/IM2009v073n02ABEH002445 (Mi im2643) 		 
This article is cited in 62 scientific papers (total in 62 papers)

Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations

A. G. Baskakov

Voronezh State University
English version PDF (738 kB) Citations (62)
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DOI: https://doi.org/10.1070/IM2009v073n02ABEH002445
Abstract: We study linear differential operators with unbounded operator-valued coefficients acting on homogeneous spaces of functions on the semi-axis. We obtain necessary and sufficient conditions for such operators to be invertible or Fredholm. Essential use is made of the spectral theory of difference relations and semigroups of linear relations (multi-valued linear operators).
Keywords: linear differential operators, spectrum of an operator, homogeneous spaces of functions, Green function, Fredholm operator.
Received: 28.03.2007
Revised: 21.11.2007
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2009, Volume 73, Issue 2, Pages 3–68
DOI: https://doi.org/10.4213/im2643
Bibliographic databases:
UDC: 517.937+517.983
MSC: 47A06, 47A53, 47D06, 34D09, 34G10, 35P05
Language: English
Original paper language: Russian
Citation: A. G. Baskakov, “Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations”, Izv. RAN. Ser. Mat., 73:2 (2009), 3–68; Izv. Math., 73:2 (2009), 215–278
Citation in format AMSBIB
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    • This publication is cited in the following 62 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:145
    First page:31
     
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