The Weyl asymptotic formula by the method of Tulovskiĭ and Shubin

• Autorzy: Paweł Głowacki
• Języki publikacji: EN

Abstrakty

EN

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 $|∂^{α}a| ≤ C_αa^{1-ϱ}$ for some ϱ>0 and all |α|>0, $∂^{α}a$ is bounded for large |α|, and $lim_{w→∞}a(w) = ∞$. 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.

Kategorie tematyczne

• 47G30: Pseudodifferential operators
• 35P20: Asymptotic distribution of eigenvalues and eigenfunctions
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 127
• Numer: 2
• Strony: 169-190

Daty

wydano

1998

otrzymano

1997-02-10

Twórcy

autor

Paweł Głowacki

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland,

Bibliografia

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