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Spectral properties of the twisted bi-Laplacian

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Abstract

The eigenvalues and eigenfunctions of the twisted bi-Laplacian are studied in the context of analytic number theory. The essential self-adjointness and the global hypoellipticity in terms of a new family of Sobolev spaces are also studied.

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References

  • Dasgupta A., Wong M.W.: Essential self-adjointness and global hypoellipticity of the twisted Laplacian. Rend. Sem. Mat. Univ. Pol. Torino 66, 75–85 (2008)

    MATH  MathSciNet  Google Scholar 

  • M. de Gosson, Phase-space Weyl calculus and global hypoellipticity of a class of degenerate elliptic partial differential operators, in: New Developments in Pseudo-Differential Operators, Operator Theory: Advances and Applications 189, Birkhäuser, 2009, 1–14.

  • Folland G.B.: Harmonic Analysis in Phase Space. Princeton University Press, New Jersey (1989)

    MATH  Google Scholar 

  • T. Gramchev, S. Pilipović, and L. Rodino, Classes of degenerate elliptic operators in Gelfand–Shilov spaces, in: New Developments in Pseudo-Differential Operators, Operator Theory: Advances and Applications 189, Birkhäuser, Basel, 2009, 15–31.

  • B. Helffer, Théorie spectrale pour des opérateurs globalment elliptiques, Astérisque 112, 1984

  • Iwaniec H., Mozzochi C.J.: On the divisor and circle problems. J. Number Theory 29, 60–93 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • W. M. Lioen, and J. van de Lune, From universal morphisms to megabytes: a Baayen space odyssey, in: Math. Centrum, Centrum Wisk. Inform., Amsterdam, 1994, 421–432

  • M. Reed and B. Simon, Fourier Analysis, Self-Adjointness, Academic Press, 1975.

  • Shubin M.A.: Pseudodifferential Operators and Spectral Theory. Springer-Verlag, Berlin (1987)

    MATH  Google Scholar 

  • Thangavelu S.: Harmonic Analysis on the Heisenberg Group. Birkhäuser, Basel (1998)

    MATH  Google Scholar 

  • Torres-Vega G., Frederick J.H.: Quantum mechanics in phase space: New approaches to the corresponding principle. J. Chem. Phys. 93, 8862–8874 (1990)

    Article  MathSciNet  Google Scholar 

  • Torres-Vega G., Frederick J.H.: A new quantum mechanical representation in phase space. J. Chem. Phys. 98, 3103–3120 (1993)

    Article  Google Scholar 

  • Wong M.W.: Weyl Transforms. Springer-Verlag, Berlin (1999)

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy

    Todor Gramchev

  2. Department of Mathematics and Informatics, University of Novi Sad, Trg D. Obradovića 4, 21000, Novi Sad, Serbia

    Stevan Pilipović

  3. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Turin, Italy

    Luigi Rodino

  4. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    M. W. Wong

Authors
  1. Todor Gramchev
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  2. Stevan Pilipović
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  3. Luigi Rodino
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  4. M. W. Wong
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Corresponding author

Correspondence to M. W. Wong.

Additional information

The research of M. W. Wong has been supported by the Natural Sciences and Engineering Research Council of Canada.

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Gramchev, T., Pilipović, S., Rodino, L. et al. Spectral properties of the twisted bi-Laplacian. Arch. Math. 93, 565–575 (2009). https://doi.org/10.1007/s00013-009-0073-9

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  • DOI: https://doi.org/10.1007/s00013-009-0073-9

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