Spectrum of a non-self-adjoint operator associated with the periodic heat equation
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چکیده
منابع مشابه
Spectrum of a non-self-adjoint operator associated with the periodic heat equation
We study the spectrum of the linear operator L = −∂θ − ǫ∂θ(sin θ∂θ) subject to the periodic boundary conditions on θ ∈ [−π, π]. We prove that the operator is closed in L2([−π, π]) with the domain in H per([−π, π]) for |ǫ| < 2, its spectrum consists of an infinite sequence of isolated eigenvalues and the set of corresponding eigenfunctions is complete. By using numerical approximations of eigenv...
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In this paper has been studied the wave equation in some non-classic cases. In the rst case boundary conditions are non-local and non-periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers,in which two ...
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Pauli’s well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamiltonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate t...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.12.036