|
Matematicheskie Zametki, 1969, Volume 5, Issue 2, Pages 245–251
(Mi mzm6829)
|
|
|
|
The asymptotic behavior of the spectral function for elliptic operators in an unbounded region
G. I. Bass Serpukhov Engineering High School
Abstract:
We consider elliptic self-adjoint differential operators L of order 2m in a bounded region D⊂Rn. An asymptotic formula for the function N(λ)=∑λn<λ1 the number of eigenvalues of the operator L less than λ is proved:
N(λ)=M0λn/2m+o(λn/2m)
where λ→+∞ and M0 is the following constant:
M0=VD(2π)nΓ(1+n/2m)∫Rne−L(s)ds.
Received: 28.02.1968
Citation:
G. I. Bass, “The asymptotic behavior of the spectral function for elliptic operators in an unbounded region”, Mat. Zametki, 5:2 (1969), 245–251; Math. Notes, 5:2 (1969), 149–152
Linking options:
https://www.mathnet.ru/eng/mzm6829 https://www.mathnet.ru/eng/mzm/v5/i2/p245
|
Statistics & downloads: |
Abstract page: | 233 | Full-text PDF : | 82 | First page: | 1 |
|