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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Sobolev space estimates for solutions of equations with delay, and the basis of divided differences


Authors: V. V. Vlasov and S. A. Ivanov
Translated by: B. M. Bekker
Original publication: Algebra i Analiz, tom 15 (2003), nomer 4.
Journal: St. Petersburg Math. J. 15 (2004), 545-561
MSC (2000): Primary 34K40, 42B30, 46E35
Published electronically: July 6, 2004
MathSciNet review: 2068981
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Abstract | References | Similar Articles | Additional Information

Abstract: Sharp Sobolev space estimates for solutions of neutral difference-differential equations with arbitrary index are obtained without the assumption that the roots of the characteristic quasipolynomial are separated. The proof is based on the fact that the system of divided differences of the exponential solutions forms a Riesz basis. Moreover, it is proved that, under more general conditions, the system of exponential solutions is minimal and complete.


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Additional Information

V. V. Vlasov
Affiliation: Moscow State University, Vorobyovy Gory, Moscow 119992, Russia
Email: vlasov@math.mipt.ru, vvvlasov2002@mail.ru

S. A. Ivanov
Affiliation: St. Petersburg State University, Russian Center of Laser Physics, Ulyanovskaya 1, Petrodvorets, St. Petersburg 198904, Russia
Email: Sergei.Ivanov@pobox.spbu.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-04-00821-0
PII: S 1061-0022(04)00821-0
Keywords: Equations with delay, exponential families, Riesz basis, Sobolev space
Received by editor(s): February 18, 2003
Published electronically: July 6, 2004
Additional Notes: Supported by RFFR (grants nos. 02-01-00790, 00-15-96100, 02-01-00554).
Article copyright: © Copyright 2004 American Mathematical Society