Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

A third order operator with periodic coefficients on the real line


Authors: A. V. Badanin and E. L. Korotyaev
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 25 (2013), nomer 5.
Journal: St. Petersburg Math. J. 25 (2014), 713-734
MSC (2010): Primary 34L40
DOI: https://doi.org/10.1090/S1061-0022-2014-01313-1
Published electronically: July 18, 2014
MathSciNet review: 3184605
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The operator $ i\partial ^3+i \partial p+i p\partial +q$ with 1-periodic coefficients $ p,q\in L_{\mathrm {loc}}^1(\mathbb{R})$ is considered on the real line. The following results are obtained: 1) the spectrum of this operator is absolutely continuous, covers the entire real line, and has multiplicity one or three; 2) the spectrum of multiplicity three is bounded and expressed in terms of real zeros of a certain entire function; 3) the Lyapunov function, analytic on a 3-sheeted Riemann surface, is constructed and investigated.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 34L40

Retrieve articles in all journals with MSC (2010): 34L40


Additional Information

A. V. Badanin
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 2, Staryi Peterhof, St. Petersburg 198904, Russia
Email: an.badanin@gmail.com

E. L. Korotyaev
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 2, Staryi Peterhof, St. Petersburg 198904, Russia
Email: korotyaev@gmail.com

DOI: https://doi.org/10.1090/S1061-0022-2014-01313-1
Keywords: Periodic third order operator, spectral bands, spectral asymptotics
Received by editor(s): October 15, 2012
Published electronically: July 18, 2014
Additional Notes: Supported by the RF Ministry of Education and Science (the federal program “Scientific and pedagogical potential of innovative Russia”, 2009–2013), contract no. 14.740.11.0581. The second author was also supported by RFBR, grant “Spectral and asymptotic methods of studying differential operators” (no. 11-01-00458).
Article copyright: © Copyright 2014 American Mathematical Society

American Mathematical Society