Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the dual boundary conditions of the fourth derivative operators

Author: Peng-Fei Yao
Journal: Quart. Appl. Math. 54 (1996), 445-456
MSC: Primary 47N20; Secondary 34B15, 35G15, 47E05
DOI: https://doi.org/10.1090/qam/1402404
MathSciNet review: MR1402404
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Abstract: A dual relationship between the boundary condition of the fourth derivative operator

$\displaystyle Au = \frac{{{\partial ^4}u}}{{\partial {x^4}}}$

is established and examined in this paper. Some dual properties determined by the dual boundary conditions are also considered.

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

  • [1] D. L. Russell, On the positive square root of the fourth derivative operator, Quart. Appl. Math. XLVI, 751-773 (1988)
  • [2] P. F. Yao and D. X. Feng, Structure for nonnegative square roots of unbounded nonnegative selfadjoint operators, to appear, this journal
  • [3] Joachim Weidmann, Linear operators in Hilbert spaces, Springer-Verlag, New York, Heidelberg, Berlin, 1980

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DOI: https://doi.org/10.1090/qam/1402404
Article copyright: © Copyright 1996 American Mathematical Society

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