Spectral analysis of differential operators with unbounded periodic coefficients

To a linear differential operator (respectively, equation) with unbounded periodic coefficients in a Banach space of vector functions defined on the entire real line, we assign a difference operator (respectively, a difference equation) with a constant operator coefficient defined in the correspondi...

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Bibliographic Details
Published in:Differential equations 2015-03, Vol.51 (3), p.325-341
Main Authors: Baskakov, A. G., Didenko, V. B.
Format: Article
Language:English
Subjects:
Algebra
Banach space
Banach spaces
Cauchy problems
Constants
Difference and Functional Equations
Difference equations
Differential equations
Hilbert space
Kernels
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Spectra
Studies
Theorems
Vectors (mathematics)
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Summary:To a linear differential operator (respectively, equation) with unbounded periodic coefficients in a Banach space of vector functions defined on the entire real line, we assign a difference operator (respectively, a difference equation) with a constant operator coefficient defined in the corresponding Banach space of two-sided vector sequences. For the differential and difference operators, we prove the coincidence of the dimensions of their kernels and coranges, the simultaneous complementability of kernels and ranges, the simultaneous invertibility, and a relationship between the spectra.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266115030052