Displaying similar documents to “Two remarks about spectral asymptotics of pseudodifferential operators”

Sharp spectral asymptotics and Weyl formula for elliptic operators with Non-smooth Coefficients-Part 2

Lech Zielinski (2002)

Colloquium Mathematicae

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We describe the asymptotic distribution of eigenvalues of self-adjoint elliptic differential operators, assuming that the first-order derivatives of the coefficients are Lipschitz continuous. We consider the asymptotic formula of Hörmander's type for the spectral function of pseudodifferential operators obtained via a regularization procedure of non-smooth coefficients.

The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

Paweł Głowacki (1998)

Studia Mathematica

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Let A be a pseudodifferential operator on ℝ N whose Weyl symbol a is a strictly positive smooth function on W = ℝ N × ℝ N such that | ∂ α a | ≤ C α a 1 - ϱ for some ϱ>0 and all |α|>0, ∂ α a is bounded for large |α|, and l i m w → ∞ a ( w ) = ∞ . Such an operator A is essentially selfadjoint, bounded from below, and its spectrum is discrete. The remainder term in the Weyl asymptotic formula for the distribution of the eigenvalues of A is estimated. This is done by applying the method of approximate spectral projectors of Tulovskiĭ and Shubin. ...

Semiclassical distribution of eigenvalues for elliptic operators with Hölder continuous coefficients, part i: non-critical case

Lech Zieliński (2004)

Colloquium Mathematicae

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We consider a version of the Weyl formula describing the asymptotic behaviour of the counting function of eigenvalues in the semiclassical approximation for self-adjoint elliptic differential operators under weak regularity hypotheses. Our aim is to treat Hölder continuous coefficients and to investigate the case of critical energy values as well.

Fredholm properties of elliptic operators on ℝⁿ

Daniel M. Elton

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We study the Fredholm properties of a general class of elliptic differential operators on ℝⁿ. These results are expressed in terms of a class of weighted function spaces, which can be locally modeled on a wide variety of standard function spaces, and a related spectral pencil problem on the sphere, which is defined in terms of the asymptotic behaviour of the coefficients of the original operator.

Analytic index formulas for elliptic corner operators

Boris Fedosov, Bert-Wolfgang Schulze, Nikolai Tarkhanov (2002)

Annales de l’institut Fourier

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Spaces with corner singularities, locally modelled by cones with base spaces having conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise smooth geometry. We consider a typical case of a manifold with corners, the so-called "edged spindle", and a natural algebra of pseudodifferential operators on it with special degeneracy in the symbols, the "corner algebra". There are three levels of principal symbols in the corner algebra, namely...