On the principal eigenvalue of a second order linear elliptic problem with an indefinite weight function

1982 ◽  
Vol 179 (2) ◽  
pp. 237-239 ◽  
Author(s):  
Peter Hess
Keyword(s):  
Weight Function ◽  
Elliptic Problem ◽  
Principal Eigenvalue ◽  
Second Order ◽  
Indefinite Weight ◽  
Order Linear ◽  
Indefinite Weight Function ◽  
Linear Elliptic Problem

scholarly journals On the eigenvalue asymptotics for a nonselfadjoint elliptic problem involving an indefinite weight

1995 ◽  
Vol 125 (4) ◽  
pp. 859-875 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Weight Function ◽  
Elliptic Problem ◽  
Distribution Functions ◽  
Indefinite Weight ◽  
Oblique Derivative Problem ◽  
Eigenvalue Asymptotics ◽  
The Real ◽  
Derivative Problem ◽  
Asymptotic Formulae ◽  
Indefinite Weight Function

We derive asymptotic formulae for the distribution functions of the real parts of the eigenvalues of an oblique derivative problem involving an indefinite weight function.

Sturm-Liouville operators with an indefinite weight function

1977 ◽  
Vol 78 (1-2) ◽  
pp. 161-191 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Weight Function ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Scalar Product ◽  
Main Tool ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Sturm Liouville ◽  
Liouville Operators

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.

Some remarks on a paper by W. N. Everitt

1977 ◽  
Vol 78 (1-2) ◽  
pp. 71-79 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Hilbert Space ◽  
Weight Function ◽  
Selfadjoint Operator ◽  
Krein Space ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Kreĭn Space ◽  
Pontrjagin Space

Everitt has shown [1[, that for α ∊ [0, π/2] the undernoted problem (1.1–2) with an indefinite weight function r can be represented by a selfadjoint operator in a suitable Hilbert space. This result is extended to arbitrary α ∊ [0, π), replacing the Hilbert space in some cases by a Pontrjagin space with index one. The problem is also treated in the Krein space generated by the weight function r.

Sign in / Sign up

Export Citation Format

Share Document